ID: Class: 12Subject: MathTopic: Application of DerivativeType: Short
Question:
It is given that at \(x = 1\), the function \(f(x) = x^4 - 62x^2 + ax + 9\) attains its maximum value on the interval \([0, 2]\).
Find the value of \(a\).
Official Solution
Explanation:
We are given:
\[
f(x) = x^4 - 62x^2 + ax + 9
\]
Differentiate:
\[
f'(x) = 4x^3 - 124x + a
\]
Since \(f(x)\) has a maximum at \(x = 1\), we have:
\[
f'(1) = 0
\]