1. 5.3 The Derivative of an Inverse Function

2. Remember…
If a function f has an inverse function f -1, Then f (a) = b implies that f -1(b) = a.
x’s and y’s switch!

3. The Derivative of f -1(x): So…The derivative of the inverse is the reciprocal of the derivative of the original

4. Ex 1)
Given that
y = f(x) = x3 + 2x – 3 is a one-to–one function, and thus has an inverse,
find (f -1)'(0).

5. Ex 2)
Find , if:
&

6. 5.6 The Derivative of Inverse Trig Functions

7. Ex 3)
Find y:

8. Ex 4)
Find y:

9. Ex 5)
Find y:

13. HW – 5.3 pg. 349 # 71 – 75 odds, 95 5.6 pg. 378 # 41 – 49 odds, 61 & 63

14. Let g be the function which converts from Fahrenheit to Celsius.
Ex 1)
Let g be the function which converts from Fahrenheit to Celsius.
Then g (F) = C = (5/9) (F – 32)
Find g -1:

15. Ex 3)
Find , if:
, ,
&