math

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