Question

How would I find the slope of the graph for this problem? g(x)=(4)/(x-6) at the point (7,4).

Answer 1

derivative

Explanation:

for any curve slope of tangent is its derivative value at a particular point :)
so
`g^'(x) = (0 - 4*1)/(x-6)^2` = `-4/(x-6)^2`

now place x=7 ( as the derivative is dependent only upon `x` coordinate and not `y( or g(x) )` coordinate.

we get derivative value = -4
hence slope of the tangent is -4 at the point (7,4)

Hope u find it helpful :)

Answer 2

`m=-4`

Explanation:

`•color(white)(x)m_(color(red)"tangent")=g'(x)" at x = 7"`

`g(x)=4/(x-6)=4(x-6)^(-1)`

`rArrg'(x)=-4(x-6)^-2=-4/(x-6)^2`

`rArrg'(7)=-4/1^2=-4`