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Question

Question: Let f(x) = \(\left\{ \begin{matrix} 2x^{2} + 2/x^{2}; & 0 < |x| \leq 2 \\ 1; & x = 0 \end{matrix} \r...

Let f(x) = {2x2+2/x2;0<x21;x=0 \left\{ \begin{matrix} 2x^{2} + 2/x^{2}; & 0 < |x| \leq 2 \\ 1; & x = 0 \end{matrix} \right.\ Then f(x) has

A

None of these

B

Greatest value 4

C

Neither greatest or least value

D

Least value 1 but no greatest value

Explanation

Solution

For x ® 0

2x2 + 2x2\frac{2}{x^{2}} ® ¥ also 2(x2+1x2)\left( x^{2} + \frac{1}{x^{2}} \right) ³ 4