Question

Analyze and sketch a graph of the given function.Label any intercepts, relative extrema,points of inflection and asymptotes. f(x)=x^3-3x^2+4

Answer 1

Refer to the Mathematica plot and calculation attached.

Answer 2

find the critical points critical points are defined as c such that f ' (c) = 0 or f ' (c) does not exist


solve f ' ' (x) = 0 to find inflection point

Answer 3

actually you have to show that concavity does change at f ' ' (x) = 0 , sometimes it does not