Question

f(x) = 0 if x<-3
f(x) = 4 if -3≤x<1
f(x) = -2 if 1≤x<5
f(x) = 0 if x≥5
g(x) = integral from -3 to x of f(t)dt

g(-4) = 0
g(-2) = 4
g(2) = ?
g(6) = ?
The absolute maximum of g(x) when x = ? and is the value of ?

It may be helpful to graph f(x).

I didn't flip the integral because the x is at the top, but I plotted the f(x) onto one graph and got g(-4) and g(-2) right, but when doing g(2)=-2 and g(6)=0 they were wrong. I also attempted to do each antiderivative of each f(x) but I'm not sure how to get these answers, let alone the lucky first two answers.

Answer 1

Nevermind, I found it myself by drawing the graph and doing rectangles.

g(2) = 14
g(6) = 8
x=1 with max area of 16