Find the absolute and local maximum and minimum values of f. f(t) = 6 cos(t), −3π/2 ≤ t ≤ 3π/2

Answer 1

The cosine function has maximum (1) at (π / 2) + 2kπ.

The cosine function has minimum (-1) at (3π / 2) = 2kπ

Answer 2

f ' (t) = -6 sin (t) on domain [-3*pi/2, 3*pi/2] = [90,270]

the derivative is zero when t = 180=pi or t = -180=-pi or t=0

the critical point is (0, -6) as 6*cos(180) = 6*-1 = -6

or (0,6) as -6* cos (-pi) = -6 *-1 = 6 , so (0,6) is the absolute max.

f(-3*pi/2) = 6 * cos * (-3*pi/2) = 6 * cos(90) = 0

f(3 *pi/2) = 6 * cos(270) = 0

are the solutions

absolute min (0, -6)