Calculus Question

Question

Let g(x) = x	f(t) dt
0

,

 where f is the function whose graph is shown.

(a) Evaluate g(0), g(4), g(8), g(12), and g(24).

g(0)	=
g(4)	=
g(8)	=
g(12)	=
g(24)	=

(b) On what interval is g increasing? (Enter your answer using interval notation.)

[4,8]∪[24,28]

 

 

(c) Where does g have a maximum value?

x =  

(d) Sketch a rough graph of g.

Answer 1

I'm assuming you mean that g(x) = ∫₀^x f(t)dt. In that case, then:

a. We can solve these expressions by adding and subtracting the areas of the graph:

g(0) = 0, g(4) = 32, g(8) = 80, g(12) = 112, g(24) = 48

b. g(x) is increasing in the interval (0, 12) since the areas of f(x) are positive in that interval.

c. g(x) has a maximum at x = 12.

d. The bottom left graph looks like the right graph of g(x) based on our previous answers.