Give the value of c in the interval [0,2] that satisfies the conclusion of the mean value theorem for :

Question

g(x) = -2 -/x 2

answers:

a) -1

b) 1

c) 2

d) -3/2

e) 1/2

i have several questions like this that i need to answer but am not sure how its done. Could someone explain just this one to me please.

Thanks

Answer 1

1. This should be posted in Math, not Economics.

2. I don't understand your formula so let's use: g(x) = 2x^3 over the interval [-1, 1]

g(-1) = -2, g(+1) = +2, so we are looking for a c such that

g'(c) = (g(+1) - g(-1))/(1 - -1) = 4/2 = 2

http://en.wikipedia.org/wiki/Mean_value_...

The derivative of g(x) with respect to x = 6x^2 so:

6c^2 = 2, c^2= 2/6 = 1/3

so there are two values of c: 1/sqrt(3) and -1/sqrt(3)