The function x^2 x in the interval (1, e) has - Vidyadip

MCQ

The function ${x^2}\log x$ in the interval $ (1, e)$ has

A
A point of maximum
B
A point of minimum
C
Points of maximum as well as of minimum
✓
Neither a point of maximum nor minimum

✓

Answer

Correct option: D.

Neither a point of maximum nor minimum

d
(d) Let $f(x) = {x^2}\log x$ ==> $f'(x) = 2x\log x + x$

and $f''(x) = 2(1 + \log x) + 1$

Now $f''(1) = 3 + 2{\log _e}1$ and $f''(e) = 3 + 2{\log _e}e$

$f(x)$ has local minimum at $\frac{1}{{\sqrt e }}$,

but $x$ lies only in interval $(1,e)$ so that ${y_2} = \sqrt x $ has not extremum in $(1,e).$

Hence neither a point of maximum nor minimum.

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