SOLUTION: Please help!!!
Find the critical values,points of inflection and discuss the concavity of the graph of
f(x)=(x-1)^3(x+3)
and then sketch a neat graph of f,showing all the sal
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-> SOLUTION: Please help!!!
Find the critical values,points of inflection and discuss the concavity of the graph of
f(x)=(x-1)^3(x+3)
and then sketch a neat graph of f,showing all the sal
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Question 1093170: Please help!!!
Find the critical values,points of inflection and discuss the concavity of the graph of
f(x)=(x-1)^3(x+3)
and then sketch a neat graph of f,showing all the salient points. Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! f(x)=(x-1)^3(x+3)
f'(x)=(x-1)^3+3(x-1)^2(x+3)=x^3-3x^2+3x-1+3(x^3+x^2-5x+3)=4x^3-12x+8
that is 4(x^3-3x+2)=4(x+2)(x^2-2x+1)
Set equal to 0, and critical points are at x=-2 y=-27 and x=1 y=0
second derivative is 4(3x^2-3)=4(x^2-1), so inflection points are where x=1 and -1, because the second derivative is 0.
Where x=-2, y is positive so a minimum.
first derivative graph
