CBSE 2026 · Region 3 · Set 3 · Q23 · 2 marks
Find the sub-interval of $\displaystyle (0, \infty)$ in which $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x} \log \mathrm{x}$ is increasing.
Marking-scheme solution
$\displaystyle \mathrm{f}(x)=x \log x \Rightarrow \mathrm{f}^{\prime}(x)=1+\log x$
Put $\displaystyle 1+\log x=0 \Rightarrow x=\dfrac{1}{e}$
$\displaystyle \because \mathrm{f}^{\prime}(x)>0\ \forall x \in\left(\dfrac{1}{e}, \infty\right) \Rightarrow \mathrm{f}(x)$ is increasing in $\displaystyle \left(\dfrac{1}{e}, \infty\right)$.
Application of DerivativesIncreasing and Decreasing FunctionsApplyvery_short_answereasy
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 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.