it is assumed that f is differentiable and that w has an absolute maximum at t0

Question

w(t)= f(t)/(c+t)

derivative is f'(t)(c+t)-f(t)/(c+t)^2

Show that f(t0) = f′(t0)(C + t0).

I'm having a bit of trouble in the above question. I keep getting f(t0)= (c+t0)-f'(t0) instead of f(t0) = f′(t0)(C + t0).

Help is always appreciated :)

Answer 1

if w has a max at t0, dw/dt = 0 at t0.

so,

(f'(t0)(c+t0)-f(t0))/(c+t0)^2 = 0