OPTIONAL EXTRA CREDIT- AP Calc Fall Final Review

What is the limit?

• Infinity
• 20
• DNE
• 12

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.B.4

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

If the position of a particle is represented by s(t) = -t² + 1, what is its position at t = 1? 

• Position = 0
• Position = 1
• Position = 2
• Position = -1 

Tags

CCSS.6.EE.B.5

What is the derivative of sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

What is the derivative of cos(x)?

• sin(x)
• -sin(x)
• cos(x)
• -cos(x)

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

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

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

Tags

CCSS.HSA.APR.A.1

Given  $f\left(x\right)=\frac{x^3}{1-x^2}$  , what is  $f'\left(x\right)$  ?

•  $\frac{x^2\left(3-5x^2\right)}{\left(1-x^2\right)^2}$  

•  $\frac{3x^2-x^4}{\left(1-x^2\right)}$  

•  $\frac{-3x^2+x^4}{\left(1-x^4\right)}$  

•  $\frac{x^2\left(3-x^2\right)}{\left(1-x^2\right)^2}$  

Find the slope of the line tangent to  $f$  at  $x=9$  given  $f\left(x\right)=-x^2+5\sqrt{x}$  

•  $18+\frac{5}{6}$  

•  $-18+\frac{5}{6}$  

•  $-18-\frac{5}{6}$  

•  $18-\frac{5}{6}$  

 $f$  be the function given by  $f\left(x\right)=x^3.$  What are all values of  $c$  that satisfy the conclusion of the Mean Value Theorem on the closed interval  $\left[-1,2\right]$  ?

•  $1$   only

•  $\sqrt{3}$   only

•  $-1$  and $1$  

•  $-\sqrt{3}$  and  $\sqrt{3}$