If f(x)=(\frac{5}{2})x^{\frac{2}{3}}-x^{\frac{5}{3}}, what are the points of inflection, concavity and

Travis Caldwell

Travis Caldwell

Answered question

2022-04-22

If f(x)=(52)x23x53, what are the points of inflection, concavity and critical points?

Answer & Explanation

diehaterzh8s

diehaterzh8s

Beginner2022-04-23Added 11 answers

Step 1
f(x)=(52)x23x53
The domain of f is (,).
f(x)=(53)x1353x23
=53[x13x23]
=53[1xx13]
f' does not exist at x=0 and f(x)=0 at x=1. Both 0 and 1 are in the domain of f, so both are critical numbers.
Step 2
fx)=53[13x4323x13]
=59x43[1+2x]
=5(1+2x)9x43
fx)>0 for x<12 and
fx)>0 for 12<x<0 and x>0
The graph of f is concave up on (,12) and concave down on (12,0).
The point (12,f(12)) is an inflection point.

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?