✓ Board-verified
Mathematics · 2026 · 2 marks
CBSE 2026 · Region 5 · Set 2 · Q23
Determine the interval(s) in which f ( x )=5 x^3 / 2-3 x^5 / 2, x >0 is increasing.
Determine the interval(s) in which $\displaystyle \mathrm{f}(\mathrm{x})=5 \mathrm{x}^{3 / 2}-3 \mathrm{x}^{5 / 2}, \mathrm{x}>0$ is increasing.
Marking-scheme solution
$\displaystyle f^{\prime}(x)=\dfrac{15 x^{\frac{1}{2}}}{2}-\dfrac{15 x^{\frac{3}{2}}}{2}$
$\displaystyle f^{\prime}(x)=0$ gives $\displaystyle x=1$ as $\displaystyle x>0$
Sign of $\displaystyle f^{\prime}(x)$:
$\displaystyle f(x)$ is increasing in $\displaystyle (0,1)$ or $\displaystyle (0,1]$
All Application of Derivatives questions2026 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 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.