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
Respond to this Question
Similar Questions

calculus
Find the relative max and relative min and the point of inflection, yintercept for y  x^3  9x^2 + 15x. Then sketch its graph. 
calculus ..>steve
Given a function f(x)2/3x^3+5/2x^23x. a) Find i. The inflection point. ii. The yintercept and xintercept. b) Sketch the graph of f(x). i have already try it..but i don't understand.. which graph that is true.. the first or second … 
calculus
I needed help with these FRQ in my APCalc course. Any help or walkthrough would be extremely helpful  thanks in advance. Let f be the function given by f(x)=3ln((x^2)+2)2x with the domain [2,4]. (a) Find the coordinate of each relative … 
Calculus
Let f(x) be a polynomial function such that f(2)=5, f'(2)=0, and f"(2)=3. The point (2,5) is a(n)____of the graph f. A. Relative maximum B. Relative minimum C. Intercept D. Point of Inflection E. None of these 
Calculus
Let f(x) be a polynomial function such that f(2)=5, f’(2)=0 and f”(2)=3. The point (2, 5) is which of the following for the graph of f? 
Calculus
Let f(x) be a polynomial function such that f(4)=1, f’(4)=2 and f”(4)=0. If x<4, then f”(x)<0 and if x>4, then f”(x)>0. The point (4, 1) is which of the following for the graph of f? 
Calculus check
Let f(x) be a polynomial function such that f(3)=3, f'(3)=0 and f"(3)=3. What is the point (3,3) on the graph y=f(x)? 
Calculus
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 0. Which of the following statements is false? 
calculus
If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true? 
Calculus really quick check
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 2. Which of the following statements must be true?