Regina R.

Calculus 3

1 year, 7 months ago

Let
g(x) =
x
0
f(t) dt,
where f is the function whose graph is shown.
Six line segments are connected to form the function labeled f on the t y coordinate plane. The first line segment is horizontal and starts on the y-axis at the value y = 8, goes right and ends at the point (4, 8). The second line segment starts at the point (4, 8), goes up and right and ends at the point (8, 16). The third line segment starts at the point (8, 16), goes down and right and ends at the point (12, 0). The fourth line segment starts at the point (12, 0), goes down and right and ends at the point (20, ?8). The fifth line segment is horizontal and starts at the point (20, ?8), goes right and ends at the point (24, ?8). The sixth line segment starts at the point (24, ?8), goes up and right and ends at the point (28, 0).
(a)
Evaluate g(0), g(4), g(8), g(12), and g(24).
g(0) =
0
g(4) =
20
g(8) =
g(12) =
8
g(24) =
(b)
On what interval is g increasing? (Enter your answer using interval notation.)
g(28) =
(c)
Where does g have a maximum value?
x =
(d)
Sketch a rough graph of g.