Consider the function f:(0,2) R defined by f(x)=x 2 +2 x and the … - Vidyadip

MCQ

Consider the function $f:(0,2) \rightarrow R$ defined by $f(x)=\frac{x}{2}+\frac{2}{x}$ and the function $g(x)$ defined by

A
g is continuous but not differentiable at x = 1
B
g is not continuous for all $x \in(0,2)$
C
g is neither continuous nor differentiable at x = 1
D
g is continuous and differentiable for all $x \in(0,2)$

✓

Answer

$f:(0,2) \rightarrow R ; f(x)=\frac{x}{2}+\frac{2}{x}$
$f^{\prime}(x)=\frac{1}{2}-\frac{2}{x^2}$
$\therefore f ( x )$ is decreasing in domain.

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