Suppose f(x)=αx^2+βx+γ
is a general quadratic polynomial with α≠0 and let [a,b] be any interval. According to the Mean Value Theorem there is at least one number c such that f(b)−f(a)=f′(c)(b−a).
In this particular case the number c is unique and it's independent of the coefficients of f.
c=____
Your answer will be in terms of a and b.
1 answer
see the related questions below.