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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Presentation transcript:

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 line F’(x) or y’ or dy/dx Instantaneous 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:

Answer:

Find the derivative:

Answer:

Find the derivative:

Answer:

Find the slope of the tangent line to the equation at the given point: (2, 14)

Answer: 9

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

Answer:

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 functions Absolute value functions (rewrite as a piecewise function)

For what values is the function below not differentiable?

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.