Question

What is the maximum value that the graph of `sin^4x+cos^4x`?

Answer 1

The maximum value is `1`

Explanation:

`f(x) = sin^4x+cos^4x = (sin^2x+cos^2x)^2-2sin^2xcos^2x`

`= 1-2sin^2xcos^2x`

Notice that `2sin^2xcos^2x` cannot be negative, so

`2sin^2xcos^2x >= 0`, and

`-2sin^2xcos^2x <= 0`. So,

`1-2sin^2xcos^2x <= 1`

Also note that for some `x`, we have `sinx = 0`, so for some `x`, we get `f(x) = 1`.