Question

the function defined by f(x)=x^3-3x^2 for all real numbers x has a relative maximum at x=

Answer 1

x^3-3x^2=x^2(x-3)

one can use derivative test and check for x=-sqrt(2)

Answer 2

to get relative max., differentiate f(x) and equate it to 0
that is, f'(x)=0
this function has relative maximum at x=0.

Answer 3

as well as x=+sqrt(2) and x=0

Answer 4

not at x=sqrt 2...
only at x=0