show that the function y=x^3-3x^2+5 has a maxima at x=0 and minima at x=2

usman khan
Mar 3, 2012

#1**0 **

[input]plot( x^3-3x^2+5, x=-1..3)[/input]

[input]diff( x^3-3x^2+5, x)[/input]

[input]3*x^2-(6*x)=0[/input]

so f'( 0 )=0 and f'( 2 )

[input]diff( diff( x^3-3x^2+5, x))[/input]

[input]6*x-6=0[/input]

and f''( 0 ) <> 0, and f''( 2 )<>0

usman khan:show that the function y=x^3-3x^2+5 has a maxima at x=0 and minima at x=2

[input]plot( x^3-3x^2+5, x=-1..3)[/input]

[input]diff( x^3-3x^2+5, x)[/input]

[input]3*x^2-(6*x)=0[/input]

so f'( 0 )=0 and f'( 2 )

[input]diff( diff( x^3-3x^2+5, x))[/input]

[input]6*x-6=0[/input]

and f''( 0 ) <> 0, and f''( 2 )<>0

admin
Mar 3, 2012