Find the slope of the curve at the indicated point.
-$$y = \frac { 6 } { 5 + x } , x = 9$$
A) $m = \frac { 3 } { 7 }$
B) $m = - \frac { 3 } { 98 }$
C) $\mathrm { m } = \frac { 3 } { 98 }$
D) $m = - \frac { 3 } { 7 }$

Question

Quizplus · Accepted Answer

To find the slope of the curve at a given point, we first need to differentiate the function with respect to $x$. The derivative of $y = \frac{6}{5 + x}$ using the quotient rule or recognizing it as a constant times the derivative of $1/(5+x)$ is $y' = -\frac{6}{(5 + x)^2}$. Substituting $x = 9$ into the derivative gives $y' = -\frac{6}{(5 + 9)^2} = -\frac{6}{14^2} = -\frac{6}{196} = -\frac{3}{98}$, which is the slope of the curve at the point where $x = 9$.

Find the Slope of the Curve at the Indicated Point y=65+x,x=9y = \frac { 6 } { 5 + x } , x = 9y=5+x6​,x=9

Find the Slope of the Curve at the Indicated Point $y = \frac { 6 } { 5 + x } , x = 9$