Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
-$$f ( x ) = 2 + 8 x - x 2 ; ( - 5,5 )$$
A) local maximum at $( - 4,50 )$
B) local minimum at $( - 4,18 )$
C) local maximum at $( 4,18 )$
D) local minimum at $( 4,50 )$

Question

Quizplus · Accepted Answer

The function $f(x) = 2 + 8x - x^2$ is a downward-opening parabola because the coefficient of $x^2$ is negative. The vertex of this parabola, given by the formula $(-b/2a, f(-b/2a))$ where $a = -1$ and $b = 8$, is at $x = -8/(-2) = 4$. Substituting $x = 4$ into the function gives $f(4) = 2 + 8(4) - (4)^2 = 2 + 32 - 16 = 18$. Therefore, the vertex at $(4, 18)$ is a local maximum because the parabola opens downward.

Use a Graphing Utility to Graph the Function Over the Indicated