Posted by **Britney** on Sunday, November 11, 2012 at 9:46pm.

f(x)=x^4-4x^3+10

Where are the relative extrema, if they exist?

- math -
**Reiny**, Sunday, November 11, 2012 at 11:23pm
from your previous post

x = 0 or x = 3

so

f(0) = 10

f(3) = 81 - 108 + 10 = -17

f '' (x) = 12x^2 - 24x

f '(0) = f ''(0) = 0

so (0,10) is a point of inflection

f ''(3) = 108 - 72 > 0

so at (3,-17) the curve is concave upwards, so

(3,-17) is a minimum point

look at the sketch

http://www.wolframalpha.com/input/?i=plot+x%5E4-4x%5E3%2B10

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