Intro to Calculus - Week 25 Quiz Multiple Choice Section

Given v(t) = x^-9, find the general equation for the antiderivative.

• (1/8)x^-8 + C
• (-1/8)x^-8 + C
• (1/10)x¹⁰
• (-1/8)x^-8

Find the antiderivative of
x²

• (1/3)x³+C
• x³
• (1/3)x³
• 2x

Given v(t) = -sin(2x), determine the general for the antiderivative.

• cos(2x)
• 2cos(2x)
• -cos(2x)
• 1/2cos(2x)

f'(x) = (x + 2)/(3x). f(x) =

• (2/3)ln|x| + x/3 + C
• 2ln|3x| + x/3 + C
• (2/3)ln|x| + C
• (2/3)ln|3x| + C

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Find the derivative f(x) = xe^x 

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

Find the derivative of  $y=\ln3x$  

•  $\frac{1}{x}$  

•  $\frac{1}{3x}$  

•  $\ln3\ +\ \ln x$  

•  $\frac{1}{\ln3x}$  

Find the derivative of  $y=e^{\tan x}$  

•  $e^{\tan x}$  

•  $e^{\sec^2x}$  

•  $\tan xe^{\sec x-1}$  

•  $\sec^2xe^{\tan x}$  

Find all values of c that satisfy the MVT for the function on the given interval

f(x) = -x² + 8x - 17 on [2,6]

• c = 2

• c = 3

• c = 4

• c = 6

Tags

CCSS.HSA.REI.D.11

If f '(x) changes from negative to positive, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

Tags

CCSS.HSA.APR.B.3