Is \(\displaystyle{f{{\left({x}\right)}}}={x}{\left({x}-{2}\right)}{\left({x}+{3}\right)}{\left({x}-{1}\right)}\) concave or convex at

Angelina Kaufman

Angelina Kaufman

Answered question

2022-04-15

Is f(x)=x(x2)(x+3)(x1) concave or convex at x=1?

Answer & Explanation

Vegljamzt6

Vegljamzt6

Beginner2022-04-16Added 16 answers

Step 1
This problem may be easier if we determine the expanded (not factored) form of f(x) first.
f(x)=x(x2)(x+3)(x1)=x(x2+x6)(x1)=x(x37x+6)=x47x2+6x
=x47x2+6x
f(x)=4x314x+6
Step 2
and f(x)=12x214
f(1)=121214=2
Which means that f(x) is concave DOWNWARDS (convex?) at x=1 because f1)<0

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?