Question

Find the extreme values of cos 2x + cos square x

Answer 1

4 is the correct answer beacuse when you use the formula for cos2x you will get 1+3cos²x and the maximum values of cos x is 1 and -1 so th extremum valuse of the function is 4 and -2

Answer 2

Answer:

The extreme values are $\frac{n\pi}{2}$, where n belongs to integer.

Step-by-step explanation:

The`given function is

$f(x)=\cos 2x+\cos^2x$

$f'(x)=-2\sin 2x-2\cos x\sin x$

$f'(x)=-2\sin 2x-2\sin 2x$                 $[\because \sin 2x=2\sin x \cos x]$

$f'(x)=-4\sin 2x$

To find the extreme values equate f'(x) equal to 0.

$f'(x)=0$

$-4\sin 2x=0$

$\sin 2x=0$

$2x=n\pi$

$2x=\frac{n\pi}{2}$

Therefore the extreme values are $\frac{n\pi}{2}$, where n belongs to integer.