Subject: Graphing regions
Who is asking: Parent
Question: This is the second of two questions my son had problems with.
Find the area of the region enclosed by the graphs of y = x3-6x and y = -2x between their points of intersection.Hi Esther,
Let f(x) = x3-6x and g(x) = -2x. First you need to find where the curves intersect. Solving f(x) = g(x) gives
x(x2 - 4) = 0
x = -2, 0 or 2
Now between x = -2 and x = 0 and between x = 0 and x = 2 you need to determine "which curve is on top and which is on the bottom", that is which function f or g is larger.
Choose a point between x = -2 and x = 0, say x = -1.
g(-1) = -2(-1) = 2
Choose a point between x = 0 and x = 2, say x = 1.
g(-1) = -2(1) = -2