A Function and Its Graph Are Given $y = f ( x )$

question 56

Multiple Choice

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of $y = f ( x )$ . Check these results against the graph shown. $$y = 18 x ^ { 4 } - 54 x ^ { 2 } + 36$$

• A) \(x = - \frac { \sqrt { 2 } } { 2 }\)
• B) \(x = 0\)
• C) \(x = \frac { \sqrt { 2 } } { 2 }\)
• D) \(x = \frac { \sqrt { 2 } } { 2 }\) , \(x = - \frac { \sqrt { 2 } } { 2 }\)
• E) \(x = - \frac { \sqrt { 2 } } { 2 }\) , \(x = 0\) , \(x = - \frac { \sqrt { 2 } } { 2 }\)

---

Definitions:

Regret

A feeling of sadness, repentance, or disappointment over something that has happened or been done.

Standard Deck

A pack of playing cards, typically comprising 52 cards in four suits, used in a variety of card games.

Without Replacement

A sampling method where once an item is selected, it is not put back into the population for potential reselection.

Consecutive Red Cards

In card games or sports like soccer, instances where red cards are issued in sequential order, either to players or as drawn cards from a deck.