If w ( x ) = f ( x ) q ( x ) w\left(x\right)=f\left(x\right)q\left(x\right) w ( x ) = f ( x ) q ( x ) , then w ′ ( x ) = w'\left(x\right)= w ′ ( x ) =

f ′ ( x ) q ( x ) + f ( x ) q ′ ( x ) f'\left(x\right)q\left(x\right)+f\left(x\right)q'\left(x\right) f ′ ( x ) q ( x ) + f ( x ) q ′ ( x )

f ′ ( x ) q ′ ( x ) f'\left(x\right)q'\left(x\right) f ′ ( x ) q ′ ( x )

f ′ ( x ) q ′ ( x ) + f ( x ) q ( x ) f'\left(x\right)q'\left(x\right)+f\left(x\right)q\left(x\right) f ′ ( x ) q ′ ( x ) + f ( x ) q ( x )

f ′ ( q ( x ) ) q ′ ( x ) f'\left(q\left(x\right)\right)q'\left(x\right) f ′ ( q ( x ) ) q ′ ( x )

Evaluate lim ⁡ x → π 4 cos ⁡ x − cos ⁡ ( π 4 ) x − π 4 \lim_{x\rightarrow\frac{\pi}{4}}\frac{\cos x-\cos\left(\frac{\pi}{4}\right)}{x-\frac{\pi}{4}} x → 4 π lim x − 4 π cos x − cos ( 4 π )

− 2 2 -\frac{\sqrt{2}}{2} − 2 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">

2 2 \frac{\sqrt{2}}{2} 2 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">

For a particle moving along the x-axis, the particle's speed equals 2 when

∣ v ( t ) ∣ = 2 \left|v\left(t\right)\right|=2 ∣ v ( t ) ∣ = 2

v ( t ) = 2 v\left(t\right)=2 v ( t ) = 2

a ( t ) = 2 a\left(t\right)=2 a ( t ) = 2

∣ a ( t ) ∣ = 2 \left|a\left(t\right)\right|=2 ∣ a ( t ) ∣ = 2

If f ( x ) = ∫ 4 x ( cos ⁡ ( 2 t ) + 3 ) d t f\left(x\right)=\int_4^x\left(\cos\left(2t\right)+3\right)dt f ( x ) = ∫ 4 x ( cos ( 2 t ) + 3 ) d t , then f ′ ( x ) = f'\left(x\right)= f ′ ( x ) =

cos ⁡ ( 2 x ) + 3 \cos\left(2x\right)+3 cos ( 2 x ) + 3

1 2 sin ⁡ ( 2 x ) + 3 x \frac{1}{2}\sin\left(2x\right)+3x 2 1 sin ( 2 x ) + 3 x

cos ⁡ ( 2 x ) \cos\left(2x\right) cos ( 2 x )

2 cos ⁡ ( 2 x ) + 3 2\cos\left(2x\right)+3 2 cos ( 2 x ) + 3

What are the conditions that satisfy the mean value theorem, and what does it mean?

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval ( a , b ) (that is a < c < b ) such that

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

Continuous on the open and differentiable on the open, and then there is no number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

AP Calculus Final First 15 :)

Authored by Tanya Hickson

Mathematics

12th Grade

CCSS covered

Used 3+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

36 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the limit?

Infinity

DNE

Find the second derivative of the function:
f (x) = 2x - 5x⁶

f ''(x)= 2 - 30x

f ''(x) = 2-30x⁵

f ''(x) = -30x⁵

f ''(x) = -150x⁴

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Intermediate Value Theorem

Rolle's Theorem

Average Rate of Change

Average Value of f

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Average Rate of Change

Average Value of f

Intermediate Value Theorem

Rolle's Theorem

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Microsoft

or continue with

Facebook

Apple

Others

Already have an account?

Similar Resources on Wayground

31 questions

HH12C1B01 - Khối Đa Diện

Quiz

•

12th Grade

40 questions

trigonometrija

Quiz

•

10th - 12th Grade

35 questions

SKB Dikti - Matematika (sejenis TIU)

Quiz

•

12th Grade - Professi...

39 questions

" Grand Quizz Seconde " (Semaine des Mathémathématiques 2017)

Quiz

•

1st - 12th Grade

39 questions

Unit 9 Review

Quiz

•

9th - 12th Grade

40 questions

US Matematika Wajib

Quiz

•

9th - 12th Grade

40 questions

TRY OUT UN MATEMATIKA SMA/MA IPS

Quiz

•

12th Grade

35 questions

Campeonato de cálculo mental 1

Quiz

•

1st - 12th Grade

Popular Resources on Wayground

10 questions

Oak Hills High School Policy and Success Quiz

Passage

•

9th Grade

11 questions

Hallway & Bathroom Expectations

Quiz

•

6th - 8th Grade

15 questions

School Bus Safety Questions

Quiz

•

6th Grade

25 questions

AJHS Scavenger Hunt

Quiz

•

6th Grade

20 questions

Lab Safety Quiz

Quiz

•

6th Grade

22 questions

would you rather

Quiz

•

3rd - 11th Grade

29 questions

Laboratory Safety Rules

Quiz

•

6th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

Discover more resources for Mathematics

20 questions

Function or Not? Domain and Range

Quiz

•

9th - 12th Grade

23 questions

Six Parent Functions

Quiz

•

9th - 12th Grade

19 questions

Classify Types of Real Numbers

Quiz

•

9th - 12th Grade

17 questions

Geometry Vocabulary Basics

Quiz

•

9th - 12th Grade

20 questions

1.1 (b) Add / Sub/ Multiply Polynomials

Quiz

•

12th Grade

20 questions

Squares and Square Roots

Quiz

•

9th - 12th Grade

40 questions

Algebra Review Topics

Quiz

•

9th - 12th Grade

12 questions

Classifying Polys - 1.1

Quiz

•

10th - 12th Grade

AP Calculus Final First 15 :)

What is the limit?

Find the second derivative of the function:f (x) = 2x - 5x6

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the second derivative of the function:
f (x) = 2x - 5x⁶