Question

If at \( x = 1 \), the function \( x^4 - 62x^2 + ax + 9 \) attains its maximum value on the interval \( [0, 2] \), then the value of \( a \) is:

• A. 110
• B. 10
• C. 55
• D. None of these

Hint:

To find the maximum or minimum value of a function, take the derivative and solve for critical points, then check the value at those points.

Answer 1

The Correct Option is C

Step 1: To find the value of \( a \), differentiate the function and find the critical points.
Step 2: By substituting \( x = 1 \) into the function and ensuring that it is a maximum, we solve for \( a \), which gives \( a = 55 \).

Final Answer: \[ \boxed{55} \]