In which of the following, function f(x)=x^2-4 x +6 is increasing… - Vidyadip

MCQ

In which of the following, function $f(x)=x^2-4 x$ +6 is increasing :

A
$(-\infty, 2) \cup(2, \infty)$
B
$(2, \infty)$
C
$(-\infty, 2)$
D
$(-\infty, 2] \cup(2, \infty)$

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Answer

(B)Here $\quad f(x)=x^2-4 x+6$
$\therefore \quad f^{\prime}(x)=2 x-4$
now,$\quad f^{\prime}(x)=0 \Rightarrow 2 x-4=0 \Rightarrow x=2$

$\because \quad f^{\prime}(x)>0 \forall x \in(2, \infty)$
$\therefore f(x)$ is increasing in interval $(2, \infty)$

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