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

Jan 15, 2018

derivative

#### Explanation:

for any curve slope of tangent is its derivative value at a particular point :)
so
${g}^{'} \left(x\right) = \frac{0 - 4 \cdot 1}{x - 6} ^ 2$ = $- \frac{4}{x - 6} ^ 2$

now place x=7 ( as the derivative is dependent only upon $x$ coordinate and not $y \left(\mathmr{and} g \left(x\right)\right)$ coordinate.

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

Hope u find it helpful :)

Jan 15, 2018

$m = - 4$

#### Explanation:

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

$g \left(x\right) = \frac{4}{x - 6} = 4 {\left(x - 6\right)}^{- 1}$

$\Rightarrow g ' \left(x\right) = - 4 {\left(x - 6\right)}^{-} 2 = - \frac{4}{x - 6} ^ 2$

$\Rightarrow g ' \left(7\right) = - \frac{4}{1} ^ 2 = - 4$