CBSE 2024 · Region 1 · Set 2 · Q25 · 2 marks
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
$$\mathrm{f}^{\prime}(\mathrm{x})=16 \mathrm{x}^{\frac{1}{3}}-\frac{2}{\mathrm{x}^{\frac{2}{3}}}
For critical points, $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})=0$
\Rightarrow 16 \mathrm{x}=2 \Rightarrow \mathrm{x}=\frac{1}{8}
$$
Application of DerivativesMaxima and MinimaApplyvery_short_answermedium
More from Application of Derivatives
- Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and…2024 · asked 3×
- Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is…2024 · asked 3×
- A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed…2025 · asked 3×
- At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup…2026 · asked 3×
- A company produces cylindrical tumblers, open from the top. Since they want uniformity in the product, they…2026 · asked 3×
- Sooraj's father wants to construct a rectangular garden using a brick wall on one side of the garden and wire…2023 · asked 3×
- If f(x)=a(x- cos x) is strictly decreasing in R, then ' a ' belongs to2023 · asked 3×
- A tank, as shown in the figure below, formed using a combination of a cylinder and a cone, offers better…2023 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.