Derivatives of Polynomials and Exponential Functions

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Presentation transcript:

Derivatives of Polynomials and Exponential Functions Section 3.1

Power Functions For n = 4 we find the derivative of f (x) = x4 as follows:

Example 1, power rule If f (x) = x6, then f (x) = 6x5. (b) If y = x1000, then y = 1000x999. (c) If y = t 4, then = 4t 3. (d) = 3r 2

Example 2, differentiate

Example 3, Tangent & Normal

Example 3, Tangent & Normal Tangent Line Normal Line

Example 4, constant multiple

Example 5, derivative

Example 6, horizontal tangent

Example 6, horizontal tangent

Example 7, Acceleration

Example 8 If f (x) = ex – x, find f  and f .

3.1 Derivatives of Polynomials and Exponential Functions Summarize Notes Read section 3.1 Homework Pg.181 #7,9,11,15,19,23,29,34,36,43,44,47,49,51

Find the 1st derivative

Find the 1st derivative

Find the 1st derivative

Find the Tangent and Normal lines

Find the Tangent and Normal lines

Find the Velocity and Acceleration Find acceleration at 1 second.

Find Horizontal Tangents