Given that ƒ''(x) = cos(x), ƒ'(π/2) = 11 and ƒ(π/2) = 11, find: ƒ'(x) and ƒ(x)

Question

Given that ƒ''(x) = cos(x), ƒ'(π/2) = 11 and ƒ(π/2) = 11, find:

ƒ'(x) =

ƒ(x) =

Answer 1

Integrate once to turn f ''(x) into f'(x) and use (π/2, 11) to solve for C. Integrate a second time to get f(x) and again use (π/2, 11) to solve for the second constant.

I'll start:

∫f''(x) = ∫cos(x)

f '(x) = sin(x) + C

11 = sin(π/2) + C

11 = 1 + C

C = 10

f '(x) = sin(x) + 10

Repeat the process to get f(x)