How do you determine whether the function

Angelina Kaufman

Angelina Kaufman

Answered question

2022-04-18

How do you determine whether the function F(x)=x+1x is concave up or concave down and its intervals?

Answer & Explanation

fallendreamsit2p

fallendreamsit2p

Beginner2022-04-19Added 14 answers

Step 1
For f(x)=x+1x, we get f(x)=11x2 and fx)=2x3 which is negative for x<0 and positive for x>0.
Step 2
So the graph of f is concave down on (,0) and concave up on (0,)
There is no inflection point because the concavity changes at x=0 which is not in the domain of f.

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