Answer each question appropriately.
-How many curves $y = f ( x )$ have the following properties?
i. $\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } 2 } = 7 \mathrm { x }$
ii. The graph passes through the point $( 0,3 )$ and has a horizontal tangent at that point.
A) Infinitely many
B) 1
C) 0
D) 2

Question

Quizplus · Accepted Answer

The second derivative $\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } 2 } = 7 \mathrm { x }$ implies the first derivative is $ \frac { \mathrm { dy } } { \mathrm { dx } } = \frac{7}{2}x^2 + C$. For a horizontal tangent at $(0,3)$, $C = 0$. Integrating again gives $y = \frac{7}{6}x^3 + 3$, which satisfies all conditions.

Answer Each Question Appropriately y=f(x)y = f ( x )y=f(x) Have the Following Properties? I

Answer Each Question Appropriately $y = f ( x )$ Have the Following Properties?
I