How many points of inflection are on the graph of the function? $f(x)=18 x^{3}+5 x^{2}-12 x-20$
A) 5
B) 2
C) 3
D) 4
E) 1

Question

Quizplus · Accepted Answer

A point of inflection occurs where the second derivative changes sign. For $f(x)=18x^3+5x^2-12x-20$, the second derivative is $f''(x)=108x+10$. Setting $f''(x)=0$ gives $x=-\frac{10}{108}=-\frac{5}{54}$. Since this is a linear function, it changes sign at this point, indicating one point of inflection.

How Many Points of Inflection Are on the Graph of the Function