Chapter 5, Problem 21CCSR

Solution

To graph : The cat's path in the first quadrant and to find the furthest point of cat from the pole if the pole is at $\left(2,0\right)$ .

Given information :

A cat ran around part of a telephone pole on a path modeled by the equation $y=-x^2+4x-1$ .

Graph :

The graph of the cat's path in the first quadrantusing graphing calculator is given below:

  

To find the furthest point of cat from the pole if the pole is at $\left(2,0\right)$ find the relative maxima and for this select the analyse function and copy the popup information text as below:

Analysis of the function $y=-x^2+4x-1$

Minimum of $x=-10$

Maximum of $x=10$

Accuracy (decimal signs) $=5$

Number of steps $=200$

  $y\text{'}=-2x+4$

Zeros of the function $=2$

  $\begin{array}{l}0.26795\\ 3.73205\end{array}$

Extrema: $1$

	$x$	$y$
Max	$2$	$3$

Interpretation :

The furthest point of cat from the pole if the pole is at $\left(2,0\right)$ is $\left(2,3\right)$ .