For what values of $c$ does the curve have maximum and minimum points?
$$F ( x ) = 4 x ^ { 3 } + c x ^ { 2 } + 10 x$$
A) $| c | 40$
B) $| c | \sqrt { 1200 }$
C) $| c | \sqrt { 120 }$
D) $| c | 12$
E) $| c | \sqrt { 30 }$

Question

For what values of $c$ does the curve have maximum and minimum points?
$$F ( x ) = 4 x ^ { 3 } + c x ^ { 2 } + 10 x$$
A) $| c | > 40$
B) $| c | > \sqrt { 1200 }$
C) $| c | > \sqrt { 120 }$
D) $| c | > 12$
E) $| c | > \sqrt { 30 }$

Quizplus · Accepted Answer

The correct answer is C because the discriminant of the quadratic equation $F'(x) = 0$ must be negative for the curve to have maximum and minimum points. The discriminant is $c^2 - 160$, so $|c| > \sqrt{120}$.

For What Values Of ccc Does the Curve Have Maximum and Minimum Points

For What Values Of $c$ Does the Curve Have Maximum and Minimum Points