# Thread: quick Calc Equation question

1. ## quick Calc Equation question

Hello,
I am stuck with this one question, I do not even know how to begin. Any help would be greatly appreciated.

Determine $\displaystyle a$, $\displaystyle b$, $\displaystyle c$ and $\displaystyle d$ so that the graph of $\displaystyle ax^3+bx^2+cx+d$ has a point of inflection at the origin and a relative maximum at the point $\displaystyle (2,4)$.

I know the point of inflection is when the second derivative equals 0 and the max is when the first derivative equals 0, going from negative y values to positive y values. but how do i use that?

2. Originally Posted by OnMyWayToBeAMathProffesor
Hello,
I am stuck with this one question, I do not even know how to begin. Any help would be greatly appreciated.

Determine $\displaystyle a$, $\displaystyle b$, $\displaystyle c$ and $\displaystyle d$ so that the graph of $\displaystyle ax^3+bx^2+cx+d$ has a point of inflection at the origin and a relative maximum at the point $\displaystyle (2,4)$.

I know the point of inflection is when the second derivative equals 0 and the max is when the first derivative equals 0, going from negative y values to positive y values. but how do i use that?

Let f(x) = ax3 + bx2 + cx + d
f'(x) = 3ax2 + 2bx + c
f''(x) = 6ax + 2b

f(2) = 8a + 4b + 2c + d = 8a + 2c = 4
f'(2) = 12a + 4b + c = 12a + c = 0

Solve

8a + 2c - 2(12a + c) = 4 - 0
-16a = 4
a = -1/4

12(-1/4) + c = 0
c = 3

Therefore, f(x) = -1/4 x3 + 3x

3. This question was answered yesterday here: http://www.mathhelpforum.com/math-he...213-b-c-d.html