AP EAMCET · Maths · Application of Derivatives
The interval in which the function \(f(x)=2 x^2-\log x\), for \(x>0\) decreases, is
- A (2, 4)
- B \(\left(0, \frac{1}{4}\right)\)
- C \(\left(\frac{1}{2}, \infty\right)\)
- D \(\left(0, \frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(0, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=2 x^2-\log x, x>0 \] Differentiate w.r.t ' \(x\) ' \[ f^{\prime}(x)=4 x-\frac{1}{x}=\frac{4 x^2-1}{x} \] Now, \(\quad f^{\prime}(x)=0\) \[ 4 x^2-1=0 \] \[ 4 x^2=1 \] \[ \Rightarrow x= \pm \frac{1}{2} \] for decreasing…
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