Question

What is the inflection point of

f(x) = 2x-3x^(2/3)

Answer 1

The inflection point is associated with the vanishing of the 2nd derivative, are you familiar with derivatives?

Answer 2

Try finding the first derivative, and then we'll move on from there.

Answer 3

Mhmm I am

Answer 4

2-2x^(-1/3)

Answer 5

That's right!

Answer 6

We'll need to take the derivative of this to get the 2nd derivative

Answer 7

Then for the 2nd deriv I get 2/3*x^(-4/3)

Answer 8

Wait think I dropped the -

Answer 9

-2/3x^(-4/3)

Answer 10

Yep

Answer 11

Do you just set that = 0? Or how do you get the inflection from here?

Answer 12

Note that the overall result here will be positive since the -2 will multiply the -1/3 exponent

Answer 13

\(\color{blue}{\text{Originally Posted by}}\) @tjb69812
Do you just set that = 0? Or how do you get the inflection from here?
\(\color{blue}{\text{End of Quote}}\)
That's right! We set y" = 0 and see if this equation has any real solutions:

Answer 14

Think this is where I'm screwing up