Application of Derivatives

CBSE Class 12 · Mathematics · 18 past questions

1. Q1 2026

   The least value of $f(x) = x^3 - 12x$, $x \in [0, 3]$ is

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2. Q2 2026

   Find the sub-interval(s) of $\left(0, \frac{\pi}{2}\right)$ in which $f(x) = \tan x - 4x$ is increasing.

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3. Q3 2025

   Find the intervals in which function $f(x) = 5x^{3/2} - 3x^{5/2}$ is (i) increasing (ii) decreasing.

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4. Q4 2025

   A technical company is designing a rectangular solar panel installation on a roof using 300 metres of… (with a figure)

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5. Q5 2025

   The function $f(x) = x^2 - 4x + 6$ is increasing in the interval

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6. Q6 2025

   A cylindrical tank of radius 10 cm is being filled with sugar at the rate of $100\pi$ cm$^3$/s. The rate, at…

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7. Q7 2025

   Find the values of 'a' for which $f(x)=\sin x-ax+b$ is increasing on $\mathbb{R}$.

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8. Q8 2025

   The values of $\lambda$ so that $f(x) = \sin x - \cos x - \lambda x + C$ decreases for all real values of x…

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9. Q9 2025

   For the curve $y=5x-2x^3$, if $x$ increases at the rate of 2 units/s, then how fast is the slope of the curve…

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10. Q10 2024

    Find the intervals in which the function $f(x) = \frac{\log x}{x}$ is strictly increasing or strictly…

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11. Q11 2024

    The function $f(x) = x^3 - 3x^2 + 12x - 18$ is…

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12. Q12 2024

    If $M$ and $m$ denote the local maximum and local minimum values of the function $f(x) = x + \frac{1}{x}$…

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13. Q13 2023

    If $f(x) = a(\tan x - \cot x)$, where $a > 0$, then find whether $f(x)$ is increasing or decreasing function…

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14. Q14 2023

    In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should… (with a figure)

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15. Q15 2023

    A volleyball player serves the ball which takes a parabolic path given by the equation… (with a figure)

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16. Q16 2023

    If $f(x) = a(x - \cos x)$ is strictly decreasing in $\mathbb{R}$, then 'a' belongs to

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17. Q17 2023

    A particle moves along the curve $3y = ax^3 + 1$ such that at a point with $x$–coordinate 1, $y$–coordinate…

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18. Q18 2023

    Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The… (with a figure)

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