JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a polynomial function of degree four having extreme values at \(x=4\) and \(x=5\).
If \(\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5\), then \(f(2)\) is equal to :
- A 12
- B 10
- C 8
- D 14
Answer & Solution
Correct Answer
(B) 10
Step-by-step Solution
Detailed 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)…
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