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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 1 · Set 2 · Q25
Find the absolute maximum and minimum values of the function f ( x )=12 x^4 / 3-6 x^1 / 3, x ∈[0,1].
Find the absolute maximum and minimum values of the function $\displaystyle \mathrm{f}(\mathrm{x})=12 \mathrm{x}^{4 / 3}-6 \mathrm{x}^{1 / 3}, \mathrm{x} \in[0,1]$.
Marking-scheme solution
$$\mathrm{f}^{\prime}(\mathrm{x})=16 \mathrm{x}^{\frac{1}{3}}-\frac{2}{\mathrm{x}^{\frac{2}{3}}}
$$
For critical points, $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})=0$
$$\Rightarrow 16 \mathrm{x}=2 \Rightarrow \mathrm{x}=\frac{1}{8}
$$
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.