TS EAMCET · Maths · Application of Derivatives
Let \(f(x)=x^3+2 x^2-x\) be a real valued function. Then, the value of Lagrange's constant \(C\) in \((-1,2)\) is
- A \(\frac{-4+\sqrt{76}}{3}\)
- B \(\frac{-2+\sqrt{19}}{3}\)
- C \(\frac{-4+\sqrt{19}}{6}\)
- D \(\frac{-2+\sqrt{19}}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{-2+\sqrt{19}}{3}\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=x^3+2 x^2-x\) Clearly, \(f(x)\) is continuous in \([-1,2]\) and differentiable in \((-1,4)\) \([\because\) polynomial functions are everywhere continuous and differentiable.] \(\therefore\) By Lagrange's mean value theorem, there exist \(C \in(-1,4)\) such that…
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