Find the intervals in which the function f given by f(x)=x^2-4 x+…

MCQ

Find the intervals in which the function $f$ given by $f(x)=x^2-4 x+6$ is strictly increasing.

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

✓

Answer

We have, $f(x)=x^2-4 x+6$
$
\Rightarrow f^{\prime}(x)=2 x-4
$
$\because f(x)$ is strictly increasing.
$
\begin{array}{ll}
\therefore & f^{\prime}(x)>0 \\
\Rightarrow & 2 x-4>0 \Rightarrow x>2 \\
\Rightarrow & x \in(2, \infty)
\end{array}
$

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