Question

use the graph of the given function to find any relative maxima and relative minima.
$f(x)=x^{3}-12x + 2$
a. maximum: $(2,-14)$
minimum: $(-2,18)$
b. no maxima or minima
c. maxima: $(-2,18)$ and $(0,0)$
minimum: $(2,-14)$
d. minimum: $(2,-14)$
maximum: $(-2,18)$

Explanation:

Step1: Identify relative maximum and minimum

A relative maximum is a point where the function changes from increasing to decreasing. A relative minimum is a point where the function changes from decreasing to increasing.
Looking at the graph, at \(x = - 2\), the function changes from increasing to decreasing. The \(y\)-value at \(x=-2\) is \(y = 18\).
At \(x = 2\), the function changes from decreasing to increasing. The \(y\)-value at \(x = 2\) is \(y=-14\).

Answer:

D. Minimum: \((2,-14)\) Maximum: \((-2,18)\)