3.2 & 3.3. State the Differentiability Theorem Answer: If a function is differentiable at x=a, then the function is continuous at x=a.

3.2 & 3.3

State the Differentiability Theorem

Answer:If a function is differentiable at x=a, then the function is continuous at x=a.

What are other terms or notations we have used to describe the derivative?

Answer:Slope of tangent lineF’(x) or y’ or dy/dxInstantaneous velocity

What can happen to a function to make it not

differentiable?

*Be able to pick these from a graph (pg144, #35)

Find the derivative:2 2( ) 7 3 4 2f x x x x

Answer:

3

414 3x

x

Find the derivative:5 2

4( )

1

x xf x

x

Answer:

8 5 4

24

2 5 2

1

x x x x

x

Find the derivative:

( ) 3f x x x

Answer:

31 12 2 2

1 12 2

3 3 3 3 3 3

2 22 2

x x x xor or

xx x

Find the slope of the tangent line to the equation at the given point:

2 5y x x (2, 14)

Answer:

9

Find the equation of the tangent line to the equation at the given point:

1 1, ,

1 8 4 4

xy

x

Answer:

1

2y x

If f(1)=4, g(1)=2, f’(1)=-4, and g’(1)=5

Find (fg)’(1)

Answer:

12

List slopes in decreasing order:

Pg. 119 #3

List slopes in increasing order:

Pg. 132 #3

Left & Right Derivatives of:Piecewise functionsAbsolute value functions (rewrite as a piecewise function)

For what values is the function below not differentiable? 2( ) 9f x x

Answer:

x = -3, x = 3

Given the graph of f(x), graph f’(x).

*Could be open ended, multiple choice, or matching.

Any problem from homework or class notes can appear on the test.