Question: f(x)=$\int_{0}^{x}{(t^{2}–1)}\cos tdt,x \in (0,\pi)$, f(x) attains local minimum value at –...

Question

f(x)= $\int_{0}^{x}{(t^{2}–1)}\cos tdt,x \in (0,\pi)$ , f(x) attains local minimum value at –

Answer 1

f '(x) ̃ (x² – 1) cos x = 0

x = 1, x = p/2

f.''(x) = cos x. 2x + (x² – 1) (– sin x)

f.''(x) = 2 cos x > 0 7 minimum

Question: f(x)=\(\int_{0}^{x}{(t^{2}–1)}\cos tdt,x \in (0,\pi)\), f(x) attains local minimum value at –...