math
posted by Britney on .
f(x)=x^44x^3+10
Where are the relative extrema, if they exist?

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%5E44x%5E3%2B10