SOLUTION: 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, l

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.

RELATED QUESTIONS
For the function f(x) = −5x^3 + 3x^5 , find all critical values and determine... (answered by josgarithmetic)

I need help with this please :) equation is f(x)= x^2 - 4x - 3 a)Graph y=f(x) in... (answered by stanbon)

Find the values of a and b so that the function f(x)=(1/3)x^3 + ax^2 +bx will have a... (answered by greenestamps)

Our class got assigned a project on polynomials involving writing a research paper and... (answered by MathLover1)

Sorry this is calculus....I really need help. Find critical points and inflection... (answered by Alan3354)

Find all relative extrema of the function: f(x) = 1/3 x^3 - 4x + 9 I could not find (answered by stanbon)

Find the absolute extrema of the function f(x)=1/2cos2x+(√3)sinx on the interval... (answered by jim_thompson5910)

Graph (and show the graph) to determine all local and absolute extrema to the nearest... (answered by josgarithmetic)

Find the absolute extrema of the function on the closed interval. f(x) = x^3 −... (answered by Edwin McCravy)