The function is defined by f(x)= cases x^ 3 -3x^ 2 , & x 1, 2x-1, & x>1

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The function

f

is defined by

f(x)= \begin{cases} x^{3}-3x^{2}, & x\le 1,\\ 2x-1, & x>1. \end{cases}

Determine whether

x=1

is an inflection point of the graph of

f

. State your conclusion and support it by indicating the concavity on each side of

x=1