I have a test tomorrow and I'm not sure how to solve this.(adsbygoogle = window.adsbygoogle || []).push({});

I need to find: inflection points, where f(x) is increasing, concave up, and local min/max points.

[tex]f(x) = 3x^4 - 4x^3[/tex]

[tex]f'(x) = 12x^3 - 12x^2[/tex]

[tex]f'(x) = 12x(x-1)[/tex]

So I get: x = 0 and x = 1 These are my critical points right? Are these the same as inflection points?

anyway: [tex]x-1 > 0 [/tex] so, I get f(x) is increasing when x>1. Or (1, Infinity)

Now I find concavity: [tex] f''(x) = 36x^2 - 24x [/tex]

[tex] 6x(6x-4)[/tex]

[tex] 6x = 0 , x = 0[/tex]and [tex] 6x-4 = 0 , x = 2/3[/tex]

So I get: f(x) is concave up from (-infinity, 0)u(2/3, infinity)

So I figured out about half of the problem. I guess what I really need help with is how to find the inflection points, and how those are different from the critical points. And also how to find the local min/max values.

Any help is really appreciated.

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# Homework Help: Could really use some help.

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