Question

. Suppose that the graph of a function is concave up for 0 < x < 9. Which of the twoexpressions below is larger? How do you know? Be sure to give a detailed explanation ofyour conclusion.f(6)-f(4) / 6-4 or f(8)-f(6) / 8-6

Answer 1

As the function is concave from 0 to 9, this means that near the extremes of this interval it are larger. Thefore the numbers numbers near the extreme will have the higher values:

$\begin{gathered} \frac{f(6)-f(4)}{6-4} \\ \frac{f(8)-f(6)}{8-6} \end{gathered}$

Since f(8) and f(6) are closer to the extreme it means that those are the larger values.