AP Calculus Quarter 1 Review

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

Tags

CCSS.HSA.APR.A.1

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

• 2
• 1/2
• -2
• -1/2

Tags

CCSS.HSF.IF.B.6

Which of the following best describes the continuity at x = 1?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find the instantaneous rate of change for f(x) at x = 2 for  $f\left(x\right)\ =-\frac{3}{4}x^4+2$  

• -24

• - $\frac{3}{2}$  

• 24

• - $\frac{3}{4}$  

• I only

• II only

• I, II, III

• None

Tags

CCSS.HSA.SSE.A.1

What is this limit?

• $\infty$

• $-\infty$

• 0

• 2/3

 $\frac{\text{d}}{\text{d}x}\left[x^2\cdot\sin\left(x\right)\right]$  

•  $x^2\cos\left(x\right)-2x\left(\sin x\right)$  

•  $-x^2\sin\left(x\right)+2x\cos\left(x\right)$  

•  $x^2\sin\left(x\right)+2x\cos\left(x\right)$  

•  $x^2\cos\left(x\right)+2x\sin\left(x\right)$  

Given the function  $g\left(x\right)=x^4-2x-8$ which of the intervals must contain a zero? 

• [-1,1]

• [0,2]

• [2,3]

• None of these intervals

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

 $\lim_{x\rightarrow5}\frac{x^2+3x-40}{x-5}=$  ___

(no calculator)

• 13

• 8

• 15

• DNE