✓ Board-verified
Mathematics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 3 · Q26
Find the interval/intervals in which the function f ( x )= sin 3 x - cos 3 x, 0< x <(π)/2 is strictly increasing.
Find the interval/intervals in which the function $\displaystyle \mathrm{f}(\mathrm{x})=\sin 3 \mathrm{x}-\cos 3 \mathrm{x}$, $\displaystyle 0<\mathrm{x}<\frac{\pi}{2}$ is strictly increasing.
Marking-scheme solution
$\displaystyle \mathbf{f}^{\prime}(\mathbf{x})=\mathbf{3} \boldsymbol{\operatorname { c o s }} \mathbf{3 x}+\mathbf{3} \boldsymbol{\operatorname { s i n }} \mathbf{3 x}$
\[\mathrm{f}^{\prime}(\mathrm{x})=0 \Rightarrow \sin 3 \mathrm{x}=-\cos 3 \mathrm{x} \Rightarrow \mathrm{x}=\frac{\pi}{4}
\]
For $\displaystyle \mathbf{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{4}}\right), \mathbf{3} \boldsymbol{\operatorname { c o s }} \mathbf{3} \mathbf{x}+\mathbf{3} \boldsymbol{\operatorname { s i n }} \mathbf{3} \mathbf{x} \boldsymbol{>} \mathbf{0}$
$\displaystyle \Rightarrow \mathbf{f}^{\prime}(\mathbf{x})>\mathbf{0}, \mathbf{f}$ is strictly increasing function in $\displaystyle \left(\mathbf{0}, \frac{\pi}{4}\right)$ or $\displaystyle \left(\mathbf{0}, \frac{\pi}{4}\right]$
All Application of Derivatives questions2025 question paperNCERT solutions: Application of DerivativesPractice Application of Derivatives →
More from Application of Derivatives
- Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach…2024
- Find the local maxima and local minima of the function f(x)=8/3 x^3-12 x^2+18 x+5.2025
- The least value of f(x)=x^3-12 x, x ∈[0,3] is2026
- Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Then, this function f(x) is strictly increasing in (a, b) if2024
- Show that the function f given by f(x)= sin x+ cos x, is strictly decreasing in the interval ((π)/4, (5 π)/4).2024
- A cylindrical tank is being filled with sand at a rate of 314 m^3 / h. If the radius of the tank is 10 m, then the height of sand in the tank…2026
- Find the sub-interval of (0, ∞) in which f(x)=x^2 e^-x is increasing.2026
- A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint…2025
CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.