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JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f (x)\) be a polynomial of degree \(4\) having extreme values at \(x\, = 1\) and \(x\, = 2\). If \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{f\left( x \right)}}{{{x^2}}} + 1} \right) = 3\) then \(f(-1)\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{5}{2}\)
- D \(\frac{9}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
\(\because f(x)\) has extremum values at \(x=1\) and \(x=2\) \(\because f^{\prime}(1)=0\) and \(f^{\prime}(2)=0\) As, \(f(x)\) is a polynomial of degree \(4\). Suppose \(f(x)=A x^{4}+B x^{3}+C x^{2}+D x+E\) \(\because \lim _{x \rightarrow 0}\left(\frac{f(x)}{x^{2}}+1\right)=3\)…
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