CBSE 2023 · Region 3 · Set 1 · Q23 · 2 marks
If $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{a}(\tan \mathrm{x}-\cot \mathrm{x})$, where $\displaystyle \mathrm{a}>0$, then find whether $\displaystyle \mathrm{f}(\mathrm{x})$ is increasing or decreasing function in its domain.
Marking-scheme solution
$$\mathrm{f}^{\prime}(\mathrm{x})=\mathrm{a}\left(\sec ^{2} \mathrm{x}+\operatorname{cosec}^{2} \mathrm{x}\right)As $\displaystyle \mathrm{a}>0$ and $\displaystyle \sec ^{2} \mathrm{x}, \operatorname{cosec}^{2} \mathrm{x}$ are squares, $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})>0$
$\displaystyle \therefore \mathrm{f}(\mathrm{x})$ is an increasing function in its domain.
Application of DerivativesIncreasing and Decreasing FunctionsApplyvery_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 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.