JEE Main 2025 — Application of Derivatives Question with Solution
JEE Main 2025 (7 Apr Shift 2)
Question
Let be a polynomial function of degree four having extreme values at and .
If , then is equal to :
If , then is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B10
Step-by-step explanation
$\begin{aligned}
& \lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5 \\ & \lim _{x \rightarrow 0} \frac{\left.a x^4+b x^3+c x^2+d x+e\right)}{x^2}=5 \\ & c=5 \text { and } d=e=0 \\ & f(x)=a x^4+b x^3+5 x^2 \\ & f^{\prime}(x)=4 a x^3+3 b x^2+10 x \\ & =x\left(4 a x^2+3 b x+10\right)
\end{aligned}f^{\prime}(4)=0 \& f^{\prime}(5)=0\mathrm{a}=\frac{1}{8} \& \mathrm{~b}=\frac{-3}{2}\text { so } f(2)=\frac{1}{8} \times 2^4-\frac{3}{2} \times 2^3+5 \times 2^2=2-12+20=10 $
& \lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5 \\ & \lim _{x \rightarrow 0} \frac{\left.a x^4+b x^3+c x^2+d x+e\right)}{x^2}=5 \\ & c=5 \text { and } d=e=0 \\ & f(x)=a x^4+b x^3+5 x^2 \\ & f^{\prime}(x)=4 a x^3+3 b x^2+10 x \\ & =x\left(4 a x^2+3 b x+10\right)
\end{aligned}f^{\prime}(4)=0 \& f^{\prime}(5)=0\mathrm{a}=\frac{1}{8} \& \mathrm{~b}=\frac{-3}{2}\text { so } f(2)=\frac{1}{8} \times 2^4-\frac{3}{2} \times 2^3+5 \times 2^2=2-12+20=10 $
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This is a previous-year question from JEE Main 2025, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.