Examples Using the Definition and Alternative Definition of the Derivative

Example 1

Find the slope of the function’s graph at the given point.

Example 2

Find the slope of the line tangent to the curve at the indicated point.

Example 3

Find the derivative of f at x=2 and x=3.

Example 4

Use the definition of the derivative to calculate the derivative of the function. Then find the values of the derivative as specified.

Example 5

Find the instantaneous rate of change of the function at the given value.

The Alternative Definition of the Derivative

Use the problem in Example 2 to calculate the derivative using the alternative definition.

More on Limits

Understanding the Definition of the Derivative

Finding Limits of Polynomial, Rational, and Radical Expressions

Proof of Lim x→0 sinx/x=1

Evaluating Limits of Trig Ratios

How do you find One Sided Limits Algebraically?

Evaluating Limits from a Graph

Evaluating Limits at Infinity

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