Let $a$ and $b$ be real numbers. The function $f$ defined as $$f(x) = ax^{3} + bx^{2} + x + 7$$ is always increasing. If $f(-1) = 0$, what is the sum of the different integer values that $b$ can take? A) 11 B) 13 C) 15 D) 17 E) 19
Let $a$ and $b$ be real numbers. The function $f$ defined as
$$f(x) = ax^{3} + bx^{2} + x + 7$$
is always increasing.
If $f(-1) = 0$, what is the sum of the different integer values that $b$ can take?
A) 11
B) 13
C) 15
D) 17
E) 19