GATE 2025 CE (CE1) – Question 48
The maximum value of the function $h(x) = -x^3 + 2x^2$ in the interval $[-1, 1.5]$ is equal to _________________________ (*rounded off to 1 decimal place*).
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Correct answer: 2.99 to 3.01
Explanation
$h'(x) = -3x^2 + 4x = x(4 - 3x)$, so the stationary points are $x = 0$ and $x = \frac{4}{3}$. The values are $h(-1) = 1 + 2 = 3$, $h(0) = 0$, $h\left(\frac{4}{3}\right) = 1.19$ and $h(1.5) = 1.125$. The maximum in the interval is 3.0, at the end point $x = -1$.