A real valued function f defined as f(x) = 2x2 - In |x| has

1.	A real valued function f defined as f(x) = 2x2 - In \|x\| has
Answer» Correct option is (C) Only two minima f(x) = 2x² - ln \|x\| f'(x) = 0 gives 4x - 1/x = 0 ⇒ 4x² = 1 ⇒ x = \(\pm\frac12\) Also, f"(x) = 4 + \(\frac1{x^2}>0\) \(\therefore\) Critical points x = -1/2 & x = 1/2 are point of minima of function f.

Answer»

Correct option is (C) Only two minima

f(x) = 2x² - ln |x|

f'(x) = 0 gives

4x - 1/x = 0

⇒ 4x² = 1

⇒ x = \(\pm\frac12\)

Also, f"(x) = 4 + \(\frac1{x^2}>0\)

\(\therefore\) Critical points x = -1/2 & x = 1/2 are point of minima of function f.

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A real valued function f defined as f(x) = 2x2 - In |x| has

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