Chapter 11.3, Problem 9E

To determine

Find the slope of the graph at given point.

Answer to Problem 9E

The approximate slope of the curve at point $(x,y)$ is $\text{Slope}=\frac{1}{2}$

Explanation of Solution

Given:

The graph given is:

  

Since, the slope of tangent drawn at any point is

  $\text{Slope}=\frac{\text{change in y}}{\text{change in x}}$

Now, from the above graph, the tangent crosses the x axis at 1 and y at $\frac{1}{2}$.So, the change in y is $\frac{1}{2}$ and also the change in x is 1.

Hence by the above formula of slope of the tangent,

  $\begin{array}{l}\text{Slope}=\frac{\frac{1}{2}}{1}\\ =\frac{1}{2}\end{array}$

Therefore, the approximate slope of the curve at point $(x,y)$ is $\text{Slope}=\frac{1}{2}$