Is \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{5}}-{2}{x}^{{4}}-{9}{x}^{{3}}-{2}{x}^{{2}}-{6}{x}\) concave or convex at

Henry Winters

Henry Winters

Answered question

2022-04-13

Is f(x)=4x52x49x32x26x concave or convex at x=1?

Answer & Explanation

carlosegundoacyg

carlosegundoacyg

Beginner2022-04-14Added 10 answers

Step 1
Concavity and convexity are determined by the sign of the second derivative:
- If f1)<0, then the function is concave at x=1.
- If f1)>0, then the function is convex at x=1.
Step 2
Find the second derivative:
f(x)=4x52x49x32x26x
f(x)=20x48x327x24x6
f(x)=80x324x254x4
Find the sign of the second derivative when x=1:
f(1)=80(1)324(1)254(1)4
=80(1)24(1)+544=8024+50=54
Since f1)<0, the function is concave at x=1. This means that it will resemble the shape.

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?