Calculus
posted by Anonymous .
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

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. 
also, my value for a is bad. I'll fix it when the rest of the correction arrives.
Respond to this Question
Similar Questions

Math: Calculus
Answer the following questions for the function f(x) = \frac{ x^3 }{ x^2  36 } defined on the interval [ 20, 16 ]. A. The function f(x) has vertical asympototes at____ and___ B. f(x) is concave up on the region___ to and____ to___ … 
Calculus
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 
Calculus
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 
Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
Calculus
Determine the xvalue for each inflection point on the graph of the following function. f(x)=3x^55x^480x^3+360x^2+1000x+850 
Calculus
Determine the xvalue for each inflection point on the graph of the following function. f(x)=3x^55x^480x^3+360x^2+1000x+850 
calculus
3. Let f be the function defined by f(x)=ln(2+sinx) for pi<=x<=2pi a. Find the absolute maximum value and the absolute minimum value of f. Show the analysis that leads to your conclusion. b. Find the xcoordinate of each inflection … 
Calculus HELP!!!
Here is the graph. h t t p : / /goo.gl/PTc2I (spaces added at the beginning so it could be added as a website) 1. Let g be the function given by g(x)=integrate from 4 to x f(t)dt. For each of g(1), g'(1), and g''(1), find the value … 
Calculus
Let g and h be any two twicedifferentiable functions that are defined for all real numbers and that satisfy the following properties for all x: I) (g(x))^2 + (h(x))^2=1 ii) g'(x)= (h(x))^2 iii) h(x)>0 iv) g(0)=0 a)Justify that … 
Calculus
Let f be a differentiable function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that I.f'(c)=0 II.f'(x)>0 when a≤x<c III.f'(x)<0 when c<x<≤b Which of the following …