Chapter 2.3, Problem 80E

Refer to the graph on p. 221. The function is given by

$f\left(x\right)=\frac{x^2-1}{x^2+x-6}$.

a. Inspect the graph and estimate the coordinates of any extrema.

b. Find $f\text{'}$ and use it to determine the critical values. (Hint: you will need the quadratic formula.) Round the x-values to the nearest hundredth.

c. Graph $f$ in the window $\left[0,0.2,0.16,0.17\right]$. Use trace or maximum to confirm your results from part (b).

d. Graph f in the window $\left[9.8,10,0.9519,0.95195\right]$. Use trace or minimum to confirm your results from part (b).

e. How close were your estimates of part (a)? Would you have been able to identify the relative minimum point without calculus?