1. ## Determining Values

This is a calc ab problem
f(x)= x^3+ax^2+bx+c
1)the graph of f has a point of inflection at (0,-2)
2)The average(mean) value of f(x) on the closed interval [0,2] is -3

a) determine values of a b and c
b) determine the calue of x that satisfies the conclusion of the Mean Value Theorem for f on the closed interval [0,3]

The first derivative is 3x^2+2ax+b
and the second is 6x+2a
so if you substitute 0=6(0)+2a
a= 0
also (0,-2) is a point so
-2=0+0+c
so c= -2
How would i find the rest of the information?

2. Hello,
Originally Posted by calc_help123
This is a calc ab problem
f(x)= x^3+ax^2+bx+c
1)the graph of f has a point of inflection at (0,-2)
2)The average(mean) value of f(x) on the closed interval [0,2] is -3

a) determine values of a b and c
b) determine the calue of x that satisfies the conclusion of the Mean Value Theorem for f on the closed interval [0,3]

The first derivative is 3x^2+2ax+b
and the second is 6x+2a
so if you substitute 0=6(0)+2a
a= 0
also (0,-2) is a point so
-2=0+0+c
so c= -2
How would i find the rest of the information?
So now you have $f(x)=x^3+bx-2$
You're left to find b.

Use 2) :
The average value m of a function f over an interval $[a,b]$ is :
$m=\frac{1}{b-a} \int_a^b f(x) ~dx$