average rate of change of g(x)= -x^2+3

[dbporter]

i just need help in gettin the following problem set up:

find and simlify an expression for the average rate of change g(x)= -x^2+3 on the interval between x and x+h

 

[skeeter]

average rate of change = (change in y)/(change in x) = [g(x+h) - g(x)]/[(x+h) - x]

 

[dbporter]

average rate of change = (change in y)/(change in x) = [g(x+h) - g(x)]/[(x+h) - x]

so when i plug my g(x) in, it should look like:

-x^2+h+3-x^2+3/-x^2+h-x^2+3 ?

i appreciate the help. just very unsure when setting up this type of problem

 

[Mrspi]

average rate of change = (change in y)/(change in x) = [g(x+h) - g(x)]/[(x+h) - x]

so when i plug my g(x) in, it should look like:

-x^2+h+3-x^2+3/-x^2+h-x^2+3 ?

i appreciate the help. just very unsure when setting up this type of problem

I'm afraid you've got some serious mistakes here.

I'd suggest taking it one step at a time.

g(x) = - x<SUP>2</SUP> + 3

To find g(x + h), replace each x with (x + h):

g(x + h) = - (x + h)<SUP>2</SUP> + 3

Now, simplify the right side. Remember that (x + h)<SUP>2</SUP> means (x + h)(x + h):

g(x + h) = - (x<SUP>2</SUP> + 2xh + h<SUP>2</SUP>) + 3
g(x + h) = -x<SUP>2</SUP> - 2xh - h<SUP>2</SUP> + 3

Ok...you are ready to substitute into Skeeter's formula:

g(x + h) - g(x)
----------------
(x + h) - x

(-x<SUP>2</SUP> - 2xh - h<SUP>2</SUP> + 3) - (-x<SUP>2</SUP> + 3)
-------------------------------
(x + h) - x

-x<SUP>2</SUP> - 2xh - h<SUP>2</SUP> + x<SUP>2</SUP> - 3
------------------------------
x + h - x

-2xh - h<SUP>2</SUP>
------------------
h

Factor "h" out of the numerator:

h (- 2x - h)
------------
h


And reduce the fraction......