((x^2)/2)-3x-(1/2);[4,6]

Question

how to do this problem

Answer 1

f(x) = (x²/2) - 3x - (1/2)

df(x)/dx = x - 3

 

Mean Value Theorem: You want to find a point c in the interval [a,b] such that:

 

df(c)/dx = (f(b)-f(a))/(b-a)

 

In the interval [4,6]:

c - 3 = (f(6)-f(4))/(6-4)

c - 3 = (0 - -4)/(6-4)

c - 3 = 2

c = 5