Identify any transitional values of $C$ at which the basic shape of the curve changes. $f(x)=x^{3}+3 c x$
A) $c=2$
B) $c=6$
C) $c=4$
D) $c=0$

Question

Quizplus · Accepted Answer

The transitional value occurs when the derivative $f'(x) = 3x^2 + 3c$ has a double root, which happens when $c = 0$, indicating a change in the number of real roots of the derivative and thus a change in the shape of the curve.

Identify Any Transitional Values Of CCC At Which the Basic Shape of the Curve Changes

Identify Any Transitional Values Of $C$ At Which the Basic Shape of the Curve Changes