It is given that at `x=1` , the function `x^4-62 x^2+a x+9` attains its maximum value on the interval `[0,\ 2]` . Find the value of `a` .

Explanation

To solve the problem, we need to find the value of \( a \) such that the function \( f(x) = x^4 - 62x^2 + ax + 9 \) attains its maximum value at \( x = 1 \) in the interval \([0, 2]\).

### Step-by-Step Solution:

1. **Find the derivative of the function**:
We start by differentiating the function \( f(x) \):
\[
f'(x) = \frac{d}{dx}(x^4 - 62x^2 + ax + 9)
...