AP EAMCET · Maths · Application of Derivatives
If \(f(x)=a \log |x|+b x^2+x\) has extreme values at \(x=-1\) and \(x=2\), then the ordered pair \((a, b)=\)
- A (2 ,-1 )
- B \(\left(2,-\frac{1}{2}\right)\)
- C \((-1,2)\)
- D \(\left(-\frac{1}{2}, 2\right)\)
Answer & Solution
Correct Answer
(B) \(\left(2,-\frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=a \cdot \log |x|+b x^2+x\) \[ \begin{aligned} & f^{\prime}(x)=a \cdot \frac{1}{|x|} \cdot \frac{x}{|x|}+b(2 x)+1 \\ & f^{\prime}(x)=\frac{a x}{|x|^2}+2 b x+1 \end{aligned} \] Given that \(x=-1\) is one of extremity of \(f(x)\).…
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