Answer:
a)
f is increasing in the interval
f is decreasing in the interval
b)
f is concave up in the interval
f is concave down in the interval
c)
x = 5 is the point of inflection.
Step-by-step explanation:
We have
(a) Find the intervals of increase or decrease.
To find where the function is increasing, we must find the interval(s) where f'(x)>0
By the rule of the derivative of a product:
since
we divide both sides by
and we get
so<em> f is increasing in the interval </em>
Similarly, we can see <em>f is decreasing in the interval
</em>
(b) Find the intervals of concavity.
The function is concave up in the interval(s) where f''>0
so <em>f is concave up in the interval
</em>
Similarly, we can see <em>f is concave down in the interval
</em>
(c) Find the point of inflection.
Since <em>f changes its concavity at x=5</em>, this point is a point of inflection.