Question

Let f be the function defined by f(x)= x^3 + ax^2 +bx + c and having the following properties.
1. the graph of f has a point of inflection at (0,-2).
2. The average value of f(x) on the closed interval (0,-2) is -3.

Determine the values of a,b and c

Answer 1

f' = 3x^2 + 2ax + b
f'' = 6x + 2a

f''(0) = -2, so
6*0 + 2a = -2
a = -1

f = x^3 - x^2 + bx + c


Hey! (0,-2) is
a) not a closed interval
b) not written as [low,hi]

Watch this space for further correct info.

Answer 2

also, my value for a is bad. I'll fix it when the rest of the correction arrives.