3-3 Differentiating Inverse Functions

3-3 Differentiating Inverse Functions

Guided Notes

Multiple Choice

The inverse of the function f(x) is written as ...

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Multiple Choice

The function  $f\left(x\right)=\sqrt{x}$  has an inverse function,  $g\left(x\right).$  Which of the following equations is the line tangent to the graph of  $g$  at the point  $\left(4,\ 16\right)$  on  $g$  ?

Hint: We already found the slope of the tangent line in Example 1. 

•  $y=\frac{1}{4}\left(x-4\right)+16$  

•  $y=\frac{1}{4}\left(x-4\right)-16$  

•  $y=4\left(x-4\right)+16$  

•  $y=4\left(x+4\right)+16$  

Multiple Choice

 $If\ f\left(x\right)=x^2+x-3\ \ then\ \left(f^{-1}\right)'\left(1\right)=?$  

•  $2$  

•  $\frac{1}{3}$  

•  $\frac{1}{4}$  

•  $0$  

Multiple Choice

 $The\ value\ of\ derivative\ of\ the\ inverse\ function\$   $of\ y=4x^3-5\ at\ \ \ x=-2\ is---$  

•  $\frac{1}{43}$  

•  $43$  

•  $53$  

•  $none$  

Multiple Choice

Find h'(3)

• -2

• 0

• 1

• 3