Question 348960
{{{graph(300,300,-7,7,-20,20,4x^3-3x^2+2)}}}

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{{{drawing(300,300,-1,1,-1,3,grid(1),circle(0,2,0.05),circle(1/2,7/4,0.05),graph(300,300,-1,1,-1,3,4x^3-3x^2+2))}}}
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The derivative of p(x) is,
{{{dp/dx=12x^2-6x}}}
The derivative equals zero when,
{{{12x^2-6x=0}}}
{{{6x(2x-1)=0}}}
Two solutions,
{{{x=0}}} where {{{p(x)=4(0)^3-3(0)^2+2=2}}}
Local maxima
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{{{2x-1=0}}}
{{{2x=1}}}
{{{x=1/2}}} where {{{p(x)=4(1/2)^3-3(1/2)^2+2=4/8-3/4+2=7/4}}}
Local minima
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From the graph you can pick out the intervals where the function is increasing and decreasing.