How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for #f(x)=x^3-3x^2+1#?
1 Answer
Dec 8, 2016
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Explanation:
Given -
#y=x^3-3x^2+1#
#dy/dx=3x^2-6x#
#(d^2y)/(dx^2)=6x-6#
At any given point, if
#dy/dx=0 => 3x^2-6x#
#3x(x-2)=0#
#3x=0#
#x=0#
#x-2=0#
#x=2#
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The function has a relative maximum.
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There is a relative minimum.
graph{x^3-3x^2+1 [-10, 10, -5, 5]}