#Mark the correct alternative in each of the following f(x) = 1 + 2 sinx + 3cos 2 x, 0 ≤ x ≤ is

Question

Philoid · Accepted Answer

f(x)=1+2sinx+3cos²x,

Differentiating f(x) with respect to x, we get

f’(x)=2cosx-6cosxsinx

Also, differentiating f’(x) with respect to x, we get

f’’(x)=-2sinx-6cos²x+6sin²x=-2sinx+12sin²x-6 (Since sin²x+cos²x=1)

For extreme points, f’(x)=0

⇒ 2cosx(1-3sinx)=0 or or

and

Hence, is a point of minima and is a point of maxima.