New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2025 · 7 Apr · Shift 2 · Q26

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2025 · 7 Apr · Shift 2 · Q26

Application of Derivatives question

2025 · 7 Apr · Shift 2 · Q26

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

Let f : ℝ

\to

ℝ be a polynomial function of degree four having extreme values at x = 4 and x = 5. If

\lim\limits_{x \to 0} \frac{f(x)}{x^2} = 5

, then f(2) is equal to :

A
8
B
10
C
12
D
14

More from Application of Derivatives

Let the function $f (x) = \frac{x}{3} + \frac{3}{x} + 3, x e q 0$ be strictly increasing in $(- \infty, α_{1}) \cup (α_{2}, \infty)$ and strictly decreasing in $(α_{3}, α_{4}) \cup (α_{4}, α_{5})$ . Then $i = 1 \sum 5 α_{i}^{2}$ …2025 · MCQ
Let $f (x) = \int_{0}^{x^{2}} \frac{t ^{2} - 8 t + 15}{e ^{t}} dt, x \in R$ . Then the numbers of local maximum and local minimum points of $f$ , respectively, are :2025 · MCQ
If the set of all values of $a$ , for which the equation $5 x^{3} - 15 x - a = 0$ has three distinct real roots, is the interval $β - 2 α$ , then $β - 2 α$ is equal to .2025 · Numerical
A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of $81 cm^{3} / min$ and the thickness of the…2025 · MCQ
Consider the region $R = {(x, y) : x \leq y \leq 9 - \frac{11}{3} x^{2}, x \geq 0}$ . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:2025 · MCQ
Let $f (x) = 2 lo g_{e} (x - 2) - x^{2} + a x + 1$ be the largest open interval in which the function $f (x) = 2 lo g_{e} (x - 2) - x^{2} + a x + 1$ is strictly increasing and (b, c) be the largest open interval, in which the function $g (x) = (x - 1)^{3} (x + 2 - a)^{2}$ is…2025 · MCQ
The sum of all local minimum values of the function $f (x) = {1 - 2 x, x 2$ is2025 · MCQ
If $5 f (x) + 4 f (\frac{1}{x}) = x^{2} - 2, \forall x e q 0$ and $y = 9 x^{2} f (x)$ , then $y$ is strictly increasing in :2024 · MCQ