Use the concavity test to determine the intervals on which the graph is concave up and concave down

y = -x^4 + 4x^3 - 4x + 1

I took it to the second derivative and got y = -12x^2 + 24x
I set that to 0 and got my x's to be 0 and 2. When I did my sine graph it seems that all of the points will be positive thus giving me no concave ups or downs? Did I do something wrong?

Question

Use the concavity test to determine the intervals on which the graph is concave up and concave down

y = -x^4 + 4x^3 - 4x + 1

I took it to the second derivative and got y = -12x^2 + 24x
I set that to 0 and got my x's to be 0 and 2. When I did my sine graph it seems that all of the points will be positive thus giving me no concave ups or downs? Did I do something wrong?

anonymous · Answer

http://www.wolframalpha.com/input/?i=-x^4+%2B+4x^3+-+4x+%2B+1

amoodarya · Answer

y''= -12x^2 + 24x
=-12 x(x-2)
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anonymous · Answer

It has points where concavity changes.

anonymous · Answer

I'm guess I must have plugged in my numbers incorrectly then when I was doing my sine chart based on amoodarya's answer?

phi · Answer

Here is a graph showing the curve, and its 2nd derivative