Posting...#35

I'm just going to do some example problems for this blog so yall can look at them and if you don't already know they will help you

1. Let f(x)=x^3+9x on [1,3].

(a) What is the average rate of change in f on [1,3]

f(3)-f(1)

Average rate=---------

3-1

=54-10

-----------

2

=22

(b) On what intervals is f ' (x) >0?

f '(x)=3x^2+9

=3(x^2+1)

Since x^2 +1 >0 for all x, f '(x)>0 for all x. Thus f ' (x)>0 on the interval of [1,3].

(c) Find a value c in the interval [1,3] such that the average rate of change in f over the interval [1,3] equals f ' (c).

f ' (c)=3c^2+9

22=3c^2+9

13=3c^2

c^2=13/3

=2.082

And....

Let g(x)=x-sin(pie x) on [0,2].

Find the Critical values of g.

g'(x)=1-pie cos (pie x)

0=1-(pie)cos((pie)x)

(pie)cos((pie)x)=1

cos((pie)x)=1/(pie)

(pie)x=cos^-1(1/pie)

cos^-1(1/pie)

x=--------------

pie

=o.397, 1.603

Can any one help me with Reames an example would help alot