Inflection point at (0, 5) for f(x) = ax^3 + bx^2 + c

[rocky8007]

I've been working on this problem, and have not been able to figure it out.

If f(x) = ax^3 + bx^2 + c has an inflection point at (0, 5), where A, B, and C are all positive constants or zero, find B and C. What values of A will satisfy the above condition?

Any help would be greatly appreciated.
Thanks

 

[pka]

From the given you know that:
\(\displaystyle \L f(0) = 5\quad \& \quad f''(0) = 0\)

 

[skeeter]

f(x)=ax^3+bx^2+c has an inflection point at (0,5) ... a, b, c > 0

f(0) = 5 ... c = 5

f'(x) = 3ax^2 + 2bx

f"(x) = 6ax + 2b
f"(0) = 0
b = 0

f"(x) = 6ax

for an inflection point to exist at x = 0, then f"(x) = 6ax must change sign at x = 0.

6ax will change sign for any real value of a except a = 0 ... in other words, a must be nonzero.