3-3 Differentiating Inverse Functions Lesson Slides

4 Slides • 5 Questions

1

3-3 Differentiating Inverse Functions

Guided Notes

2

Multiple Choice

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

1

f ^-1(x)

2

f ²(x)

3

f '(x)

4

f ⁺(x)

3

4

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.

1

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

2

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

3

$y=4\left(x-4\right)+16$

4

$y=4\left(x+4\right)+16$

5

6

Multiple Choice

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

1

$2$

2

$\frac{1}{3}$

3

$\frac{1}{4}$

4

$0$

7

Multiple Choice

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

1

$\frac{1}{43}$

2

$43$

3

$53$

4

$none$

8

9

Multiple Choice

Find h'(3)

1

-2

2

0

3

1

4

3

3-3 Differentiating Inverse Functions

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