Question
Find the intervals in which the function f given by f(x) = x2 – 4x + 6 is
- increasing
- decreasing
✓
Answer
We have
f (x) = x2 – 4x + 6
or f ′(x) = 2x – 4
Therefore, f ′(x) = 0 gives x = 2.
Now the point x = 2 divides the real line into two disjoint intervals namely, (– $\infty$, 2) and (2, $\infty$).
In the interval (– $\infty$, 2), f ′(x) = 2x – 4 < 0.
And in interval (2, $\infty$), $f^\prime(x)=2x-4>0$
$\therefore$ (i) f is increasing in (2, $\infty$)
and (ii) f is decreasing in (– $\infty$, 2)
f (x) = x2 – 4x + 6
or f ′(x) = 2x – 4
Therefore, f ′(x) = 0 gives x = 2.
Now the point x = 2 divides the real line into two disjoint intervals namely, (– $\infty$, 2) and (2, $\infty$).
In the interval (– $\infty$, 2), f ′(x) = 2x – 4 < 0.
And in interval (2, $\infty$), $f^\prime(x)=2x-4>0$
$\therefore$ (i) f is increasing in (2, $\infty$)
and (ii) f is decreasing in (– $\infty$, 2)
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