Question

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

Answer 1

0

General Formulas and Concepts:

Derivative is the slope of the tangent line

• Derivative of a constant = 0

• Derivative of cos(x) = -sin(x)

Explanation:

Step 1: Write function

f(x) = 2 + 3cos(x) (π, -1)

Step 2: Solve

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

Step 3: Define

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