Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. 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 $x = -8/(2*(-1)) = 4$. Substituting $x = 4$ into the function gives $f(4) = 2 + 8*4 - 4^2 = 2 + 32 - 16 = 18$. Therefore, the vertex at $x = 4$ is a local maximum because the parabola opens downward, and its value is $18$, making the correct answer a local maximum at (4, 18).

Use a Graphing Utility to Graph the Function Over the Indicated