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3.2 & 3.3

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

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Page 1: 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

Page 2: 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

State the Differentiability Theorem

Page 3: 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

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

Page 4: 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?

Page 5: 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

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

Page 6: 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 can happen to a function to make it not

differentiable?

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

Page 7: 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

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

Page 8: 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

Answer:

3

414 3x

x

Page 9: 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

Find the derivative:5 2

4( )

1

x xf x

x

Page 10: 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

Answer:

8 5 4

24

2 5 2

1

x x x x

x

Page 11: 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

Find the derivative:

( ) 3f x x x

Page 12: 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

Answer:

31 12 2 2

1 12 2

3 3 3 3 3 3

2 22 2

x x x xor or

xx x

Page 13: 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

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

2 5y x x (2, 14)

Page 14: 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

Answer:

9

Page 15: 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

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

1 1, ,

1 8 4 4

xy

x

Page 16: 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

Answer:

1

2y x

Page 17: 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

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

Find (fg)’(1)

Page 18: 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

Answer:

12

Page 19: 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

List slopes in decreasing order:

Pg. 119 #3

Page 20: 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

List slopes in increasing order:

Pg. 132 #3

Page 21: 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

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

Page 22: 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

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

Page 23: 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

Answer:

x = -3, x = 3

Page 24: 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

Given the graph of f(x), graph f’(x).

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

Page 25: 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

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


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