JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f( x)\) be a polynomial of degree four having extreme values at \( x=1 \) and \( x=2\) . If \(\mathop {\lim }\limits_{x \to 0} \left[ {1 + \frac{{f\left( x \right)}}{{{x^2}}}} \right] = 3\),then \(f\left( 2 \right)\) is equal to :
- A \(4\)
- B \(-8\)
- C \(-4\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{{x^2} + f\left( x \right)}}{{{x^2}}}} \right) = 3\), since, limit exits hence \({x^2} + f\left( x \right) = a{x^4} + b{x^3} + 3{x^2}\) \( \Rightarrow f\left( x \right) = a{x^4} + b{x^3} + 2{x^2}\)…
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