Find the local maximum or local minimum, if any, of the function `f(x)=sin^4x+cos^4x ,\ \ 0 lt x lt pi/2` using the first derivative test.

Explanation

To find the local maximum or local minimum of the function \( f(x) = \sin^4 x + \cos^4 x \) for \( 0 < x < \frac{\pi}{2} \) using the first derivative test, we will follow these steps:

### Step 1: Find the first derivative of \( f(x) \)

The function is given as:
\[ f(x) = \sin^4 x + \cos^4 x \]
...