Consider the function f(x)=x^3+ax^2+bx+c that has a relative minimum at x=3 and an inflection point at x=2.

Question

a). Determine the constants a and b to make the above information true for this function.
b). Find a relative maximum point of the function found in part (a) after plugging in values for a and b, given that f(0)=5.

Answer 1

f' = 3x^2 + 2ax + b
f" = 6x+2a
You know that
f"(2) = 0
12+2a = 0
a = -6
Now do the same with f'(3)=0