Section 3-1 Derivatives of Polynomials and Exponential Functions

1 Write the coefficients for the terms in the expansion of the expression.

2 Write the coefficients for the terms in the expansion of the expression.

3 Write the coefficients for the terms in the expansion of the expression.

Power Rule:

Constant Multiple Rule: The Sum Rule: The Difference Rule:

Exponential Functions:

Slope of the tangent line of an exponential function at x = 0:

4 Determine f '(0) for the equation to two decimal places.

5 Determine f '(0) for the equation to two decimal places.

Definition of e: The number such that

Derivative of the Natural Exponential Function:

Example:

Example: Find the points on the curve where the tangent is horizontal.

At what point on the curve is the tangent line parallel to the line Graph the curve and both lines.