Question 1155524: Consider f(x)=1/5x^5 +x^4 -4x^3 +3
A) Draw a graph of f, estimate all critical points, local extrema, and absolute extrema.
B) Compute the actual values of all critical points, local extrema, and absolute extrema.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! As x increases without bound + it goes to +oo
as x increases negatively without bound, it goes to - oo, because it has an odd exponent in the first term.
First derivative is x^4+4x^3-12x^2
set that equal to 0 and factor out a x^2 to get x^2(x^2+4x-12)=0
=x^2(x+6)(x-2)=0, Critical points are (-6, 0, 2)
Those are the x-values; substitute into the original function to get the y-values.
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