Find the value of c guaranteed by the mean value theorem for integrals?

Find the value of c guaranteed by the mean value theorem for integrals f(x) = - 4 / x^2





on the interval [ 1, 4 ]





The mean value theorem is: If f is continuous on the closed interval [a,b] then there exists a number c in the closed interval [a,b] such that





b


∫ f(x) dx = f(c)(b-a)


a








Not too sure what to be done here, included the theorem to see if that would help.

Find the value of c guaranteed by the mean value theorem for integrals?
Well let's just follow the formula.





int f(x) = 4/x


= 4/4 - 4/1 = -3


b - a = 4 - 1 = 3


So f(c) = 3/-3 = -1





So we need to find c such that f(c) = -1


-1 = -4 / c^2


c^2 = 4


c = 2





Could you tell me why c = -2 is not a valid solution to this problem?
Reply:The answer is 3