Question

Find the absolute maximum and minimum values of y = 3 cos(x - π/4) on the interval [0, π].

a) Max: 3, Min: -3
b) Max: -3, Min: 3
c) Max: 2, Min: -2
d) Max: -2, Min: 2

Answer 1

The absolute maximum value is 2.121 at x = 0, and the absolute minimum value is -2.121 at x = π.

Step-by-step explanation:

To find the absolute maximum and minimum values of the function y = 3 cos(x - π/4) on the interval [0, π], we need to find the critical points and endpoints, and then evaluate the function at these points.

Step 1: Find the critical points. Take the derivative of the function and set it equal to zero to find the critical points:

y' = -3sin(x - π/4) = 0

Solving for x gives: x - π/4 = 0, x = π/4

Step 2: Find the endpoints. Evaluate the function at the endpoints of the interval:

y(0) = 3 cos(0 - π/4) = 3 cos(-π/4) ≈ 2.121

y(π) = 3 cos(π - π/4) = 3 cos(3π/4) ≈ -2.121

Step 3: Compare the values. The absolute maximum value is 2.121 at x = 0, and the absolute minimum value is -2.121 at x = π.