Find f.

Question

f ''(θ) = sin(θ) + cos(θ), f(0) = 4, f '(0) = 2

Answer 1

f" = sin + cos
f' = -cos + sin + c
f = -sin - cos +c *Theta + d

at 0
f' = -cos + sin + c = -1 + c = 2 so c = 3
f' = -cos sin + 3
so
f = -1 +d = 4 so d = 5
f = -sin theta -cos theta + 3 * theta + 5