Chapter 11.3, Problem 27E

To determine

To graph: the function and the tangent line at the given point

Answer to Problem 27E

  

Explanation of Solution

Given:

  $f\left(x\right)=\sqrt{2-x}$

point $\left(1,f\left(1\right)\right)$

Calculation:

Plot $f(x)$ in your graphing calculator, and set a viewing window centered closely around $x=1.$ Follow the instructions provided with your calculator in order to utilize the "tangent" feature to plot the tangent line to the graph of the function at $(1,f(1))$ . The result should look like the graph below. With this graph, approximate the slope of this tangent line (the red line in the graph below by taking two points on the tangent line and dividing the approximate change in y value by the approximate change in $x$ value.

  $\begin{array}{l}{\text{Slope }}_{\tan }=\frac{\Delta y}{\Delta x}\\ \approx \frac{1-1.5}{1-0}\\ =-\frac{1}{2}\end{array}$

  

The slope of the tangent line to the function at $(1,f(1))\approx \frac{1}{2}$

Conclusion:

Therefore, the required graph is drawn.