What is the equation of the tangent line at x = 1 o f of o f f ( x ) = x f\left(x\right)=\ \sqrt{x} f ( x ) = x <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">

y = 1 2 x + 1 2 y=\frac{1}{2}x+\frac{1}{2} y = 2 1 x + 2 1

y = 1 2 x − 1 2 y=\frac{1}{2}x-\frac{1}{2} y = 2 1 x − 2 1

y = 2 x − 1 y=2x-1 y = 2 x − 1

If f '(x) = 0, what does that mean with respect to the tangent line?

Tangent line has a positive slope

Tangent line has a negative slope

If a function has a derivative that is negative, what does that tell you?

The concavity of the function is up

The concavity of the function is down

When we "take the derivative" of a function what are we finding?

The rate at which our struggles in Calculus are increasing.

Line Tangent to a Curve

Quiz

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.IF.B.4, HSF.IF.A.1, 8.EE.B.5

+7

Standards-aligned

Pamela Thompson

Used 93+ times

FREE Resource

20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of the given equation
f(x) = 7

7

0

7x

14

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of the given equation
f(x) = -4x

4

x

-4

0

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of the given equation
f(s) = 12 - 8s

-8x

-8s

-8

12 - 8

Find the derivative of the given equation
f(x) = x⁴

x³

4x

4x³

x⁴

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of the given equation
f(x) = 1 - x²

1 - 2x

-2x

-2

-1

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of the given equation
f(x) = x³ + x² + 3

3x² + 2x

3x + 2x

3x + 2x + 3

x³ + x²

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the derivative of xⁿ?

(n-1)xⁿ

nxⁿ⁺¹

(n+1)x^n-1

nx^n-1

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Line Tangent to a Curve

20 questions

Find the derivative of the given equation
f(x) = 7

Find the derivative of the given equation
f(x) = -4x

Find the derivative of the given equation
f(s) = 12 - 8s

Find the derivative of the given equation
f(x) = x⁴

Find the derivative of the given equation
f(x) = 1 - x²

Find the derivative of the given equation
f(x) = x³ + x² + 3

What is the derivative of xⁿ?

f’(x) = 3x+4. Find the slope of the line tangent to f(x) at the point (0, 7)

f(x) = 16x^1/4. Find f'(x)

Find the slope at x = 3 of the equation f(x) = 3x²

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Line Tangent to a Curve

20 questions

Find the derivative of the given equationf(x) = 7

Find the derivative of the given equationf(x) = -4x

Find the derivative of the given equationf(s) = 12 - 8s

Find the derivative of the given equationf(x) = x4

Find the derivative of the given equationf(x) = 1 - x2

Find the derivative of the given equationf(x) = x3 + x2 + 3

What is the derivative of xn?

f’(x) = 3x+4. Find the slope of the line tangent to f(x) at the point (0, 7)

f(x) = 16x1/4 . Find f'(x)

Find the slope at x = 3 of the equation f(x) = 3x2

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the derivative of the given equation
f(x) = 7

Find the derivative of the given equation
f(x) = -4x

Find the derivative of the given equation
f(s) = 12 - 8s

Find the derivative of the given equation
f(x) = x⁴

Find the derivative of the given equation
f(x) = 1 - x²

Find the derivative of the given equation
f(x) = x³ + x² + 3

What is the derivative of xⁿ?

f(x) = 16x^1/4. Find f'(x)

Find the slope at x = 3 of the equation f(x) = 3x²