GATE 2023 MT – Question 35
The maximum of $f(x)=4x^3-24x^2+36$ on $[-1,5]$ is ______ (nearest integer).
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Show answer and explanation
Correct answer: 36 to 36
Explanation
Stationary points satisfy $f^\prime(x)=12x(x-4)=0$, giving 0 and 4. Check these and both endpoints: $f(-1)=8$, $f(0)=36$, $f(4)=-92$, $f(5)=-64$. The maximum is **36**.