Let be the polynomial function defined on the closed interval .
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let f be the polynomial function f(x)=x3−4x defined on the closed interval [−3,3].
(a) Determine all x-coordinates in the interval [−3,3] at which the graph of f intersects the x-axis.
(b) For each subinterval of [−3,3] determined by the zeros found in part (a), indicate whether the graph of f lies above or below the x-axis and briefly justify your conclusion.
(c) Write, but do NOT evaluate, a mathematical expression involving one or more definite integrals that represents the exact area of the region bounded by the graph of f and the x-axis on [−3,3]. Clearly explain how your expression accounts for the behavior identified in part (b).