Calculus Question

Question

Let g(x) = x	f(t) dt
0

,

 where f is the function whose graph is shown.

(a) Evaluate g(x) for x = 0, 1, 2, 3, 4, 5, and 6.

g(0)	=
g(1)	=
g(2)	=
g(3)	=
g(4)	=
g(5)	=
g(6)	=

(b) Estimate g(7). (Use the midpoint to get the most precise estimate.)

g(7) = 

(c) Where does g have a maximum and a minimum value?

minimum	x	=
maximum	x	=

(d) Sketch a rough graph of g.

Answer 1

Hi,

In fact in this question, you have graph of derivative of function and need to discuss about function

you know when derivative = 0, this point shows it is maximum or minimum

Now watch the graph at point x = 1 & x = 3 derivative is 0, so

before x = 1 derivative >0 and after x = 1 derivative <0 ====> x = 1 is maximum

before x = 3 derivative <0 and after x = 3 derivative >0 ====> x = 3 is minimum

after x = 3 you see the graph is above of x-axis that it means derivative is positive so function is increasing

at x = 6 you see a maximum on the DERIVATIVE so on the function this point is inflection point that has changed concavity!

by these information you can recognize the function, it is at down of right side of sent figure.

By having the graph of function you can complete that table by approximate y

ONLY g(0) =0, g(2) = 0, g(4)=0 g(6) = 4 g(7) =6

I hope you understand the goal of this question that it is concept of DERIVATIVE.

Minoo