Chapter P, Problem 10PS

To determine

To graph: The function $f\left(x\right)=\sqrt{x}$ and label the point $\left(4,2\right)$ on the graph.

(a)

To determine

To Calculate: The slope of the line joining the points $\left(4,2\right)$ and $\left(9,3\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=\sqrt{x}$ at $\left(4,2\right)$.

(b)

To determine

To Calculate: The slope of the line joining the points $\left(4,2\right)$ and $\left(1,1\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=\sqrt{x}$ at $\left(4,2\right)$.

(c)

To determine

To Calculate: The slope of the line joining the points $\left(4,2\right)$ and $\left(4.41,2.1\right)$. Also compare the slope of the line with the slope of the tangent of curve $f\left(x\right)=\sqrt{x}$ at $\left(4,2\right)$.

(d)

To determine

To Calculate: The slope of the line joining the points $\left(4,2\right)$ and $\left(4+h,f\left(4+h\right)\right)$.

(e)

To determine

To Calculate: The slope of the tangent line at $\left(4,2\right)$ for the curve $f\left(x\right)=\sqrt{x}$ and explain how the answer is obtain.