Find the slope of the curve at the indicated point.
-$$y = \frac { 8 } { 4 + x } , x = 7$$
A) $m = - \frac { 8 } { 121 }$
B) $m = \frac { 8 } { 121 }$
C) $m = \frac { 8 } { 11 }$
D) $m = - \frac { 8 } { 11 }$

Question

Quizplus · Accepted Answer

To find the slope of the curve at the given point, we first need to differentiate the function with respect to $x$. The derivative of $y = \frac{8}{4+x}$ using the quotient rule or recognizing it as a constant times $x^{-1}$ form, is $y' = -\frac{8}{(4+x)^2}$. Substituting $x = 7$ into the derivative gives $y' = -\frac{8}{(4+7)^2} = -\frac{8}{121}$, which is the slope of the curve at the point where $x = 7$.

Find the Slope of the Curve at the Indicated Point y=84+x,x=7y = \frac { 8 } { 4 + x } , x = 7y=4+x8​,x=7

Find the Slope of the Curve at the Indicated Point $y = \frac { 8 } { 4 + x } , x = 7$