Quiz about Differentiation review

Question 1

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

Accepted Answer

-2x² - x + 9

Answer

-2x² + x + 9

Answer

2x² - x + 9

Answer

2x² - x - 9

Question 2

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

Accepted Answer

f ''(x) = -150x⁴

Answer

f ''(x)= 2 - 30x

Answer

f ''(x) = 2-30x⁵

Answer

f ''(x) = -30x⁵

Question 3

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

Accepted Answer

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

Answer

(12x³)*(10x)

Answer

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

Answer

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Question 4

Find the derivative of y = 2x² (3x - 4)

Accepted Answer

18x² - 16x

Answer

6x³ - 8x²

Answer

15x2 - 6x

Answer

6x - 4

Question 5

Differentiate f(x) =(2/ x⁵) - 5.

Accepted Answer

-10x-6

Answer

x5-3

Answer

-10x6

Answer

x5-5

Question 6

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

Accepted Answer

4x³ + 12x²- 4x

Answer

x³ + x²- x

Answer

4x³ + 12x²+ 4x

Answer

4x + 12x - 4x

Question 7

Find the derivative f(x) = xe^x

Accepted Answer

f'(x) = e^x + xe^x

Answer

f'(x) = e^x

Answer

f'(x) = xe^x + xe^x

Answer

f'(x) = e^x - xe^x

Question 8

Find the derivative of g(x)=(3x-2)/(x²+2)

Accepted Answer

(-3x²+4x +6)/(x²+2)²

Answer

9x2+2

Answer

3(x²+2)/(x²+2)²

Answer

(-3x²+10)/(x²+2)²

Question 9

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

Accepted Answer

f'(x) = 24x^-4 + 5 - e^x

Answer

f'(x) = -24x^-4 + 5 - e^x

Answer

f'(x) = 24x^-2 + 5 - e^x

Answer

f'(x) = 24x^-4 + 5 - e^x-1

Question 10

Find the derivative
f(t) = (t² + 2t)⁵

Accepted Answer

f'(t) = 5(t² + 2t)⁴(2t + 2)

Answer

f'(t) = 5(2t+2)⁴

Answer

f'(t) = 5(t² + 2t)⁴

Answer

f'(t) = 5(t² + 2t)⁴(2t)

Question 11

Find y' if y=e^3x

Accepted Answer

3e3x

Answer

e3x

Answer

e2x

Answer

0

Question 12

At which x-value is f continuous but not differentiable?

Accepted Answer

a

Answer

b

Answer

c

Answer

d

Question 13

At which point(s) will the slopes of the tangent line be zero?

Accepted Answer

at point B and D only

Answer

at C only

Answer

at points A, C and E only

Answer

at points A and E only

Question 14

Average Rate of Change is also known as...

Accepted Answer

slope

Answer

y-intercept

Answer

x-intercept

Answer

linear

Question 15

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

Accepted Answer

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

Answer

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

Answer

$$y=2x-1$$

Answer

$$y=2x$$

Question 16

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

Accepted Answer

The function is decreasing

Answer

The function is increasing

Answer

The concavity of the function is up

Answer

The concavity of the function is down

Question 17

What is the slope of the line normal to the curve y = x² + x at x = 1?

Accepted Answer

-1/3

Answer

-1

Answer

-1/2

Answer

-1/4

Question 18

Write the equation of the normal line of: $$f\left(x\right)=2x^2-\frac{1}{x}$$ at x = 1

Accepted Answer

$$y-1=-\frac{1}{5}\left(x-1\right)$$

Answer

$$y=-\frac{1}{5}x+\frac{4}{5}$$

Answer

$$y=5x-6$$

Answer

$$y-1=5\left(x-1\right)$$

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