AP Calc AB - Chapter 2 Derivative Review

Find equation of the line tangent to $f\left(x\right)=\frac{x-2}{x+3}$  at  $x=3$  .

Find $\frac{\text{d}y}{\text{d}x}$  if  $y=3x^4-\frac{3}{x^4}$  .

•  $y'=12x^3+12x^{-3}$  

•  $y'=12x^3-12x^{-3}$  

•  $y'=12x^3-12x^{-5}$  

•  $y'=12x^3+12x^{-5}$  

Find  $y'$ if $y=x^3\tan x$  .

Find  $y'$ if $y=\frac{1}{x^3\tan x}$  .

Find $\frac{d^2y}{dx^2}$  if  $y=\frac{x^2+3x}{e^x}$  .

The position of a particle moving on a horizontal line is given by $x\left(t\right)=t^3-4t^2+2t-1$  ( x in feet, t in minutes).  Find the velocity after 2 minutes.  (Use correct units.)

The position of a particle moving on a horizontal line is given by $x\left(t\right)=t^3-4t^2+2t-1$  ( x in feet, t in minutes).  Find a(2).  (Use correct units.)

The position of a particle moving on a line is given by $s\left(t\right)=\frac{1}{3}t^3-\frac{7}{2}t^2+10t+6$  ( s in meters, t in seconds).  When is the particle at rest?  (Use correct units.)