Find the value of the derivative at the indicated point. f(x)=2+3cosx, (π,-1)

0

General Formulas and Concepts:

Derivative is the slope of the tangent line

Derivative of a constant = 0Derivative of cos(x) = -sin(x)

Step-by-step explanation:

Step 1: Write function

f(x) = 2 + 3cos(x) (π, -1)

Step 2: Solve

Find 1st Derivative:                    f'(x) = -3sin(x)Substitute:                                  f'(π) = -3sin(π)Evaluate:                                    f'(π) = -3(0)Multiply:                                      f'(π) = 0

Step 3: Define

f'(π) = 0 tells us that when x = π, the slope of the tangent line is 0.

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