Use the limit process to find the slope of the graph of $\sqrt { x + 4 }$ at $( 5,3 )$.
A) $\frac { 1 } { 3 }$
B) 3
C) $\infty$
D) $\frac { 1 } { 6 }$
E) the slope is undefined at this point

Question

Quizplus · Accepted Answer

The slope of the graph of a function at a given point can be found using the derivative of the function at that point. The derivative of $\sqrt{x + 4}$ with respect to $x$ is $\frac{1}{2\sqrt{x + 4}}$. Substituting $x = 5$ into this derivative gives $\frac{1}{2\sqrt{5 + 4}} = \frac{1}{2\sqrt{9}} = \frac{1}{2 \cdot 3} = \frac{1}{6}$, which is the slope of the graph at the point $(5,3)$.

Use the Limit Process to Find the Slope of the Graph