SHW6B:  Real World Problems pp. 74-76 continued.

Definition. The Average Val ue of a function f(x)   on an interval [a, b] is defined :  

`Average Value ` = 1/(b-a)*Int(f(x),x = a .. b)

Example 1.

[Maple Plot]

`Function: `*f(x) = -x^2+1, `on the interval `*[-1, 1]

`Average Value ` = 1/2*Int(-x^2+1,x = -1 .. 1)

`Average Value ` = .6666666667

`Ave Value = .6667 = 66.67 % of Max Value`

``

`Find x-intercepts:`

f(x) = 0

-x^2+1 = 0

` x-intercept(s): `*x = -1.000000000, 1.

``

`Derivative of Function: `*`f '`(x) = -2*x

`Find bumps:`

`f '`(x) = 0

-2*x = 0

` x-bump(s): `*x = 0.

` bump point(s) ` = [0., 1.]

SHW6B: For each of the following compute the average value of the function on the given interval and sketch the graph.

Exercise 3. p. 74.

`Function: `*f(x) = 12*x-2*x^2, `on the interval `*[0, 6]

Exercise 5. p. 74.

`Function: `*f(x) = x*(4-x^2)^(1/2), `on the interval `*[0, 2]

Exercise 7. (a) p. 74.

`Function: `*f(x) = 500*x-x^2, `on the interval `*[0, 500]

Exercise 9. p. 74.

`Function: `*f(x) = x*(16-x^2)^(1/2), `on the interval `*[0, 4]

Exercise 13. p. 75.

`Function: `*f(x) = 200*x-5*x^2, `on the interval `*[0, 40]

Exercise 15. p. 76.

`Function: `*f(x) = x-3/4*x^2, `on the interval `*[0, 4/3]