Is \(\displaystyle{f{{\left({x}\right)}}}=-{2}{x}^{{{5}}}-{3}{x}^{{{4}}}+{15}{x}-{4}\) concave or convex at

Delilah Novak

Delilah Novak

Answered question

2022-04-16

Is f(x)=2x53x4+15x4 concave or convex at x=4?

Answer & Explanation

srasloavfv

srasloavfv

Beginner2022-04-17Added 6 answers

Step 1
The concavity and convexity of a function can be determined by examining the sign of a function's second derivative.
Note that: you may call concave "concave down" and convex "concave up."
We must find the function's second derivative through the power rule:
f(x)=2x53x4+15x4
f(x)=10x412x3+15
f(x)=40x336x2
The value of the second derivative at x=4 is:
f(4)=40(4)336(4)2=1984
Since this is >0, the function is convex (sometimes called concave up) at x=4

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?