Question

Given f"(x)=-25sin(5x)and f'(0)=0 and f(0)=4.

Find f(pi/2)

Answer 1

f''(x) = -25sin5x
f'(x) = 5 cos5x + c
f(x) = sin5x + cx + d

f'(0) = 0 so c = -5
f(0) = 4 so d = 4

f(x) = sin5x - 5x + 4

f(pi/2) = sin(5pi/2) - 5pi/2 + 4
= 5 - 5pi/2
= 5(1 - pi/2)