f(t) = \int_0^t \frac{x^2+11 x+24}{ 1+\cos^2(x)} dx

Question

At what value of t does the local max of f(t) occur?
t = ?

Answer 1

f'(t) = (t^2+11t+24)/(1+cos^2(t))
f'=0 when t^1+11t+24 = 0
That is, when t = -8 or -3
f"(t) = 2t+11
f"(-8) < 0, so the max is there.