# 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]}