Question

What is the average rate of change of f(x)=1/4x^2-4 over the interval from 0 to 3?

Answer 1

3/4

Explanation:

The x values are 0 and 3. Use the formula y2-y1/x2-x1

Plug in the x factors into the orginal equation. Should look like the equations below:

f(x)=1/4(0)^2-4 -------> -4

f(x)=1/4(3)^2-4 --------> -7/4Now plug it in to the formula we saved earlier.

-7/4-(-4)/3-0= -7/4+4/3= -7/4+16/4/3

Then simplify it.

9/4/3, and in this case we have a fraction in a fraction and when this happens just multiply the equation by the x variables reciprical which in this case the x is 3 so the equation is multiplied by 1/3 and you would get 9/12. Now simplify that and you get 3/4.

Answer 2

1/4

Explanation:

To find the average rate of change we find

f(3) -f(0)

----------

3-0

We need to find f(3) = 1/4 (3)^2 -4 = 1/4 (9) -4 = 9/4 -4 = -7/4

f(0) = 1/4 (0)^2 - 4 = -4

f(3) -f(0)

----------

3-0

-7/4 - (-4)

---------------

3-0

-7/4 +4

-----------

3-0

-7/4 +4

-----------

3-0

-7/4 +16/4

----------------

3

9/4

---------

3

9/12

1/4