$\text { Consider the function } f ( x ) = \sqrt { x } \text { and the point } P ( 9,3 ) \text { on the graph of } f \text {. }$ Estimate the slope $m$ of the tangent line of $f$ at $P ( 9,3 )$. Round your answer to four decimal places.
A) $\mathrm { m } = 0.1667$
B) $\mathrm { m } = 0.0832$
C) $\mathrm { m } = 0.3800$
D) $\mathrm { m } = 0.0556$
E) $\mathrm { m } = 0.0833$

Question

Quizplus · Accepted Answer

The slope of the tangent line to the curve $y = \sqrt{x}$ at any point can be found by differentiating $y$ with respect to $x$, which gives $y' = \frac{1}{2\sqrt{x}}$. Substituting $x = 9$ into this derivative gives $y' = \frac{1}{2\sqrt{9}} = \frac{1}{2 \cdot 3} = \frac{1}{6} = 0.1667$.

Consider the function f(x)=x and the point P(9,3) on the graph of f. \text { Consider the function } f ( x ) = \sqrt { x } \text { and the point } P ( 9,3 ) \text { on the graph of } f \text {. } Consider the function f(x)=x​ and the point P(9,3) on the graph of f.

$\text { Consider the function } f ( x ) = \sqrt { x } \text { and the point } P ( 9,3 ) \text { on the graph of } f \text {. }$