Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:(i) `f(x)=x^3,x in [-2,2]` (ii) `f(x)=sinx+cosx ,x in [0,pi]`(iii) `f(x)=4x-1/2x^2, x in [-2,9/2]`

Explanation

To find the absolute maximum and minimum values of the given functions in specified intervals, we will follow a systematic approach. We will differentiate the function, find the critical points, evaluate the function at the endpoints of the interval, and then compare these values to determine the absolute maximum and minimum.

### (i) Function: \( f(x) = x^3 \) in the interval \([-2, 2]\)

**Step 1: Find the derivative of the function.**
\[ f'(x) = 3x^2 \]
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