TS EAMCET · Maths · Application of Derivatives
The minimum value of the function \(f(x)=2 x^2-\ln |x|\), when \(x \geq 1\) is
- A \(\frac{1}{2}+\log 2\)
- B \(2\)
- C \(4\)
- D \(2+\log 2\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Wc have, \(f(x)=2 x^2-\ln |x|\) \(\therefore \quad f^{\prime}(x)=4 x-\frac{1}{x}\) For minima \(f^{\prime}(x)=0\) \(\begin{aligned} & \Rightarrow \quad 4 x-\frac{1}{x}=0 \Rightarrow 4 x^2-1=0 \\ & \Rightarrow \quad x= \pm \frac{1}{2} \\ & \text { But }\end{aligned}\)…
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