Question

Can someone please help me with
f(n)=sin^4x+cos^4x local max and min?

Answer 1

Use power reduction formulae.

Answer 2

Then derive.

Answer 3

can u show me? I cannot see this

Answer 4

f(x) =sin^4x+cos^4x

The angle that makes sin(x) = 0 is the same that causes cos(x) to be 1 or -1. Because these functions are raised to an even power here, the signs don't really matter. The maximum for sin(x) and cos(x) is 1 so it would seem that the maximum value would be 2. Not so, because the same angle does not make both expressions 1 at the same time.

I think the maximum value is 1.
The minimum value is 1/2, occurring when x = 45 degrees.
[sqrt(2) / 2] ^4 + [sqrt(2) / 2] ^4 = 1/2.

Answer 5

thank you very muchh