Concave or convex at \(\displaystyle{x}=-{1}\)? \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{4}{x}^{{{3}}}+{x}-{4}\)

Nancy Richmond

Nancy Richmond

Answered question

2022-03-25

Concave or convex at x=1?
f(x)=x44x3+x4

Answer & Explanation

SofZookywookeoybd

SofZookywookeoybd

Beginner2022-03-26Added 15 answers

Step 1
To find that out, we need to get the second derivative first.
Getting the first derivative.
1) f(x)=ddx(x44z3+x4)
We can easily find this using power rule.
2) f(x)=4x312x2+1
Getting the second derivative.
1) f(x)=ddx(4x312x2+1)
Use power rule again.
2) f(x)=12x224x
Now that we know the second derivative, we will evaluate f(x) at x=1 to check its concavity.
If f(x)>0, then it is concave up or convex
If f(x)<0, then it is concave down or concave
1) f(1)=12(1)224(1)
2) f(1)=12+24
3) f(1)=36
Since f(x) is 36 at x=1 and 36 is greater than 0, then f(x) is convex at x=1.

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?