Warm up: Below is a graph of f(x). Sketch the graph of f’(x)

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Presentation transcript:

Warm up: Below is a graph of f(x). Sketch the graph of f’(x)

Warm up: Below is a graph of f(x). Sketch the graph of f’(x)

Derivatives of Polynomials Section 2.2

Power Rule for a Polynomial Eg) Find the derivative function of:

Power Rule for a Polynomial Proof: Find the derivative of the general power function:

Polynomial Sum Rule Eg) Find the derivative of

Polynomial Sum Rule Proof: Find the derivative of:

Constant Multiple Rule Eg) Find the derivative of the following function:

Constant Multiple Rule Proof: Find the derivative of

Practice: Find the following derivatives a) b)

Summary: What are the three rules for derivatives we looked at today? If a function has a derivative function that is always positive, what does that mean about the function? Practice: Pg. 82, #2, 3, 5, 8, 18, 21, 26