calculus
posted by Yoona .
6. Determine a, b, c, and d so that the graph of y=ax^3+bx^2+cx+d has a point of inflection at the origin and a relative maximum at the point (2, 4). Sketch the graph.

y = ax^3 + bx^2 + cx + d
y' = 3ax^2 + 2bx + c
y'' = 6ax + 2b
y''(0) = 0
so b = 0
y'(2) = 0
so c = 12a
y(0) = 0
so d = 0
y = ax^3  12ax
y(2) = 4
so a = 1/4
y = 1/4 x^3 + 3x
y' = 3/4 x^2 + 3
y'' = 3/2 x