JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)\) be a polynomial of degree \(5\), and have extrema at \(x = 1\) and \(x = -1\). If \(\displaystyle\lim_{x \to 0} \left(\dfrac{f(x)}{x^3}\right) = -5\), then \(f(2) - f(-2)\) is equal to:
- A \(0\)
- B \(50\)
- C \(92\)
- D \(112\)
Answer & Solution
Correct Answer
(D) \(112\)
Step-by-step Solution
Detailed explanation
Let the polynomial of degree \(5\) be \(f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + k\). Given \(\displaystyle\lim_{x \to 0} \left(\dfrac{f(x)}{x^3}\right) = -5\), the terms of degree less than \(3\) must be zero, and the coefficient of \(x^3\) must be \(-5\). Thus, \(k = 0\),…
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