Let and . A technology-generated graph suggests that the two curves intersect three…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Let f(x)=x3−4x and g(x)=−x2+4. A technology-generated graph suggests that the two curves intersect three times.
(a) Determine analytically all x-coordinates at which f and g intersect.
(b) For each subinterval determined by the intersection points in part (a), identify which function has the greater value. Clearly state your reasoning.
(c) Explain why the finite region bounded by the two curves between the left-most and right-most points of intersection can be found with a single definite integral despite the fact that the curves intersect more than twice.
(d) Set up, but do NOT evaluate, a single definite integral that represents the exact area of the region described in part (c). Your integrand must reflect the proper subtraction of the two functions on the interval you selected.