How do I find concave up and concave

alparcero97oy

alparcero97oy

Answered question

2022-03-27

How do I find concave up and concave down from f(x)=x3+3x2+5x+7?

Answer & Explanation

Carter Lin

Carter Lin

Beginner2022-03-28Added 13 answers

Step 1
First find the derivative: f(x)=3x2+6x+5. Next find the second derivative: f(x)=6x+6=6(x+1). The second derivative changes sign from negative to positive as x increases through the value x=1.
Step 2
Therefore the graph of f is concave down when x<1, concave up when x>1, and has an inflection point when x=1.
The coordinates of the inflection point are (1,f(1))=(1,16).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?