Derivative Quiz Review

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

The graph of a twice-differentiable function f is shown in the figure above. Which of the following is true?

• f '(-1) < f '(1) < f '(0)

• f '(-1) < f '(0) < f '(1)

• f '(0) < f '(-1) < f '(1)

• f '(1) < f '(-1) < f '(0)

• f '(1) < f '(0) < f '(-1)

Given this graph of f'(x), on what interval(s) is f increasing?

• (-1,2)

• (0,1) U (3,4)

• (-1,0) U (1,3)

• (2,4)

This graph is of the first derivative, f' (x). On what interval(s) is the graph of    f    decreasing? Choose all the intervals that apply.

• (2,5)

•  $\left(5,\ \infty\right)$  
  

•  $\left(-\infty,0\right)$  

• (2,5)

• (0,2)

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Find the equation of the line tangent to $f\left(x\right)=e^{2x}+x^3$  at x=0. (Select all that apply)

•  $y-1=2\left(x-0\right)$  

•  $y=2x+1$  

•  $y-f\left(0\right)=f'\left(0\right)\left(x-0\right)$  

•  $y-1=-x$  

Find the equation of the line tangent to $f\left(x\right)=\tan\left(\sqrt{x}\right)$  at  $x=\pi$  ?

•  $\frac{\sec^2\left(\sqrt{\pi}\right)}{2\sqrt{\pi}}$  

•  $\frac{\sec^2\left(\sqrt{\pi}\right)}{\sqrt{\pi}}$  

•  $\frac{-\sec^2\left(\sqrt{\pi}\right)}{2\sqrt{\pi}}$  

• about -7