Find the maximum value of `(7-x)^4(2+x)^5w h e nx` lies between `-2a n d7.`

Explanation

To find the maximum value of \( (7-x)^4 (2+x)^5 \) for \( x \) in the interval \([-2, 7]\), we can use the concept of the Arithmetic Mean-Geometric Mean (AM-GM) inequality. Here’s a step-by-step solution:

### Step 1: Define the function
Let \( f(x) = (7-x)^4 (2+x)^5 \).

### Step 2: Identify the constraints
The variable \( x \) is constrained to the interval \([-2, 7]\). Therefore, we need to evaluate \( f(x) \) at the endpoints of the interval and potentially at critical points within the interval.

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