Let [f(x) = 3 ^4x + 10 ^3x + 6 ^2x - 3], [x [ - 6, 2 ]].

Question

Let $$f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$$, $$x \in \left[ { - {\pi  \over 6},{\pi  \over 2}} \right]$$. Then, f is :

Accepted Answer

$$f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3,x \in \left[ { - {\pi  \over 6},{\pi  \over 2}} \right]$$

$$f'(x) = 12{\sin ^3}x\cos x + 30{\sin ^2}x\cos x + 12\sin x\cos x$$

$$ = 6\sin x\cos x(2{\sin ^2}x + 5\sin x + 2)$$

$$ = 6\sin x\cos x(2\sin x + 1)(\sin  + 2)$$

Decreasing in $$\left( { - {\pi  \over 6},0} \right)$$

Solutions · 1