How do you determine whether the function

alahovom7ahc

alahovom7ahc

Answered question

2022-04-15

How do you determine whether the function ln(x2+10) is concave up or concave down and its intervals?

Answer & Explanation

entreblogsmc2j

entreblogsmc2j

Beginner2022-04-16Added 10 answers

Step 1
f(x)=ln(x2+10)
f(x)=2xx2+10
fx)=2(10x2)(x2+10)2
f" is never undefined and is 0 at ±10
Step 2
The sign of f" is the same as the sign of 10x2.
It is positive near 0 and negative far from 0.
So the graph of f is concave up on (10,10)
and concave down on (,10) and on (10,)
The points of inflection are: (10,ln20) and (10,ln20)

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