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

Jaylen Cantrell

Jaylen Cantrell

Answered question

2022-04-13

Is f(x)=2x52x3+3x2x+3 concave or convex at x=1?

Answer & Explanation

mislifola5vo

mislifola5vo

Beginner2022-04-14Added 11 answers

Step 1
You can tell if a function is concave or convex by the sign of its second derivative:
- If f1)<0, then f(x) is concave at x=1.
- If f1)>0, then f(x) is convex at x=1.
To find the second derivative, apply the power rule to each term twice.
f(x)=2x52x3+3x2x+3
f(x)=10x46x2+6x1
fx)=40x312x+6
Step 2
Find the sign of the second derivative at x=1:
f(1)=40(1)312(1)+6
This mostly becomes a test of keeping track of your positives and negatives.
f(1)=40(1)+12+6=40+18=58
Since this is >0, the function is convex at x=1. Convexity on a graph is characterized by a 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?