Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 6 sin ⁡ x − 3 2 x f\left(x\right)=6\sin x-3\sqrt{2}x f ( x ) = 6 sin x − 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = sin ⁡ x f\left(x\right)=\sin x f ( x ) = sin x

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = cos ⁡ x f\left(x\right)=\cos x f ( x ) = cos x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 10 sin ⁡ x + 5 2 x f\left(x\right)=10\sin x+5\sqrt{2}x f ( x ) = 1 0 sin x + 5 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = π 4 x=\frac{\pi}{4} x = 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 8 cos ⁡ x − 4 2 x f\left(x\right)=8\cos x-4\sqrt{2}x f ( x ) = 8 cos x − 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = π 4 x=\frac{\pi}{4} x = 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 18 cos ⁡ x + 9 2 x f\left(x\right)=18\cos x+9\sqrt{2}x f ( x ) = 1 8 cos x + 9 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 4 sin ⁡ x − 2 3 x f\left(x\right)=4\sin x-2\sqrt{3}x f ( x ) = 4 sin x − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = π 6 x=\frac{\pi}{6} x = 6 π

x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

x = 5 π 6 x=\frac{5\pi}{6} x = 6 5 π

x = 7 π 6 x=\frac{7\pi}{6} x = 6 7 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = − 6 cos ⁡ x + 3 3 x f\left(x\right)=-6\cos x+3\sqrt{3}x f ( x ) = − 6 cos x + 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

x = 4 π 3 x=\frac{4\pi}{3} x = 3 4 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 2 π 3 x=\frac{2\pi}{3} x = 3 2 π

x = π 3 x=\frac{\pi}{3} x = 3 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 2 sin ⁡ x − 2 x f\left(x\right)=2\sin x-2x f ( x ) = 2 sin x − 2 x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 5 cos ⁡ x − 5 x f\left(x\right)=5\cos x-5x f ( x ) = 5 cos x − 5 x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 6 sin ⁡ x − 3 x f\left(x\right)=6\sin x-3x f ( x ) = 6 sin x − 3 x . Select ALL that apply

x = π 3 x=\frac{\pi}{3} x = 3 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 2 π 3 x=\frac{2\pi}{3} x = 3 2 π

x = 4 π 3 x=\frac{4\pi}{3} x = 3 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 14 cos ⁡ x + 7 x f\left(x\right)=14\cos x+7x f ( x ) = 1 4 cos x + 7 x . Select ALL that apply

x = π 6 x=\frac{\pi}{6} x = 6 π

x = 5 π 6 x=\frac{5\pi}{6} x = 6 5 π

x = 7 π 6 x=\frac{7\pi}{6} x = 6 7 π

x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 3 sin ⁡ x + 3 cos ⁡ x f\left(x\right)=3\sin x+3\cos x f ( x ) = 3 sin x + 3 cos x . Select ALL that apply.

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

Calculus Critical Numbers, Relative and Absolute Extrema

10th Grade - University

•

26 Qs

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Calculus Critical Numbers, Relative and Absolute Extrema

Quiz

•

Mathematics

•

10th Grade - University

•

Practice Problem

•

Medium

•

CCSS

8.F.A.3, HSF.IF.A.2, HSF.TF.A.4

Standards-aligned

Adeyemi Aderinto

Used 130+ times

FREE Resource

26 questions

Show all answers

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

A is an absolute minimum

B is a relative maximum

C is an absolute minimum

D is an relative minimum

E is an relative minimum

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

(0,0) is an absolute minimum

(1,-14) is an absolute minimum

(4, 40) is an absolute maximum

(6, 10) is an relative minimum

(7, 65) is an absolute maximum

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the critical number of f(x) = 4x² – 8x + 1

x = 2

x = 0

x = 8

x = 1

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Find all the critical numbers of
f(x) = x³ – 6x² + 10.
Select ALL that apply

x = 4

x = 6

x = -2

x = 0

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Find all the critical numbers of
f(x) = 2x³ – 6x² + 12
Select ALL that apply.

x= 4

x= 0

x= -2

x= 2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

$f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$
Find all the critical numbers of f(x) above
Select ALL that apply.

x= -10

x= 20

x= -8

x= -2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

$f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$
Find the critical numbers of f(x). Select ALL that apply

x=2

x=0

x= -4

x= -2

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Calculus Critical Numbers, Relative and Absolute Extrema

26 questions

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Find the critical number of f(x) = 4x² – 8x + 1

Find all the critical numbers of
f(x) = x³ – 6x² + 10.
Select ALL that apply

Find all the critical numbers of
f(x) = 2x³ – 6x² + 12
Select ALL that apply.

$f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$
Find all the critical numbers of f(x) above
Select ALL that apply.

$f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$
Find the critical numbers of f(x). Select ALL that apply

Find all the critical numbers of
f(x) = 6x⁴ – 16x³ – 180x² + 456.
Select ALL that apply

Find all the critical numbers of f(x).
$f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13$
Select ALL that apply.

Given $\left(0\le x\le2\pi\right)$ Find ALL the critical numbers in $f\left(x\right)=6\sin x-3\sqrt{2}x$ . Select ALL that apply

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Calculus Critical Numbers, Relative and Absolute Extrema

26 questions

Use the diagram to classify relative and absolute extrema. Select ALL that apply.

Use the diagram to classify relative and absolute extrema.Select ALL that apply.

Find the critical number of f(x) = 4x2 – 8x + 1

Find all the critical numbers of f(x) = x3 – 6x2 + 10. Select ALL that apply

Find all the critical numbers off(x) = 2x3 – 6x2 + 12Select ALL that apply.

f(x)=23x3−18x2−80x+17f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17f(x)=32​x3−18x2−80x+17 Find all the critical numbers of f(x) aboveSelect ALL that apply.

f(x)=13x3+3x2+8x−5f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5f(x)=31​x3+3x2+8x−5 Find the critical numbers of f(x). Select ALL that apply

Find all the critical numbers of f(x) = 6x4 – 16x3 – 180x2 + 456.Select ALL that apply

Find all the critical numbers of f(x). f(x)=14x4−53x3−7x2+13f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13f(x)=41​x4−35​x3−7x2+13 Select ALL that apply.

Given (0≤x≤2π)\left(0\le x\le2\pi\right)(0≤x≤2π) Find ALL the critical numbers in f(x)=6sin⁡x−32xf\left(x\right)=6\sin x-3\sqrt{2}xf(x)=6sinx−32​x . Select ALL that apply

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Find the critical number of f(x) = 4x² – 8x + 1

Find all the critical numbers of
f(x) = x³ – 6x² + 10.
Select ALL that apply

Find all the critical numbers of
f(x) = 2x³ – 6x² + 12
Select ALL that apply.

$f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$
Find all the critical numbers of f(x) above
Select ALL that apply.

$f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$
Find the critical numbers of f(x). Select ALL that apply

Find all the critical numbers of
f(x) = 6x⁴ – 16x³ – 180x² + 456.
Select ALL that apply

Find all the critical numbers of f(x).
$f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13$
Select ALL that apply.

Given $\left(0\le x\le2\pi\right)$ Find ALL the critical numbers in $f\left(x\right)=6\sin x-3\sqrt{2}x$ . Select ALL that apply