If it is given that at $x = 1$, the function $f(x) = x^4 - 62x^2 + 2ax +8$ attains its maximum value on the interval [0, 2], then the value of $a$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60
Given: $f(x) = x^4 - 62x^2 + 2ax + 8$ attains maximum at $x=1$ on $[0,2]$
Derivative: $f'(x) = 4x^3 - 124x + 2a$
Maximum at $x=1 \Rightarrow f'(1) = 0$
$f'(1) = 4 - 124 + 2a = -120 + 2a = 0 \Rightarrow 2a = 120 \Rightarrow a = 60$
Answer: $a = 60$