Step 1: \ \

The function is . \ \

prime of means the first derivative of at .

First find the derivative of the function using the limit definition of derivative. \ \

Limit definition of derivative: . \ \

Derivative of the function is .

Now find prime of 3.

prime of 3 can be written as .

Substitute in the derivative of the function. \ \

prime of 3 is 36. \ \

Step 2:

Find the slope of the tangent line at .

Slope of the tangent is the derivative of the function at that point. \ \

Substitute in the derivative of the function.

The slope of the tangent line at is 60.

Solution: \ \

prime of 3 is 36. \ \

The slope of the tangent line at is 60.

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