Question

Question #b39ee

Answer 1

`- 1/(2a)`

Explanation:

graph{2/x [-10, 10, -5, 5]}

if `x = 4`, then `g(x)` = `g(4)`

= `2/4` = `1/2`

and when `x = a`, then `g(x)` = `g(a)`

= `2/a`

So, average rate of change of g(x) respect to x (actually limit of this

is the derivative of that function)

= `(Deltag(x))/(Delta x)` = `(1/2 - 2/a)/(4 -a)` = `(cancel(a- 4)/(2a))/cancel(-(a - 4))` = `(1/(2a))/-1` = `-1/(2a)`

Hope this helps.

Answer 2

`m=(4-a)/(2a^2-8a)`

`m=-1/(2a)`

Explanation:

Remember that the formula for finding the average rate of change between the two points is `(y_2-y_1)/(x_2-x_1)`

We can get our `y` coordinate by plugging the `x` values into the function.

Our coordinate would be `(4,g(4))` and `(a,g(a))`

We now calculate the `y` values.

When `x=4,`
`g(4)=2/4=>g(4)=1/2`
Our first point is at `(4,1/2)`

Similarly, when `x=a`,
`g(a)=2/a`

Our second point is at `(a,2/a)`

We now use our formula.

`m=(2/a-1/2)/(a-4)`

We try to simplify this.

`m=(2/a-1/2)/(a-4)`

=>`m=(4/(2a)-a/(2a))/(a-4)`

=>`m=((4-a)/(2a))/(a-4)`

=>`m=(4-a)/(2a)*1/(a-4)`

=>`m=(4-a)/(2a)*1/(-4+a)`

=>`m=(4-a)/(2a)*(-1)/(4-a)`

=>`m=cancel(4-a)/(2a)*(-1)/cancel(4-a)`

=>`m=1/(2a)*-1`

=>`m=-1/(2a)`

That is our answer!

You may get `m=(4-a)/(2a^2-8a)` if you did the following:

`m=(4-a)/(2a)*1/(a-4)`

=>`m=(4-a)/((2a)(a-4))`

=>`m=(4-a)/(2a^2-8a)`