the value of c guaranteed to exist by the Mean Value Theorem for V(x) = x² in the interval [0, 3] is...? a) 1 b) 2 c) 3/2 d) 1/2 e) None of the above

 c) .

Step-by-step explanation:

Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

Given function :

Interval : [0,3]

Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that

Since

then, at x=c,

From (i) and (ii), we have

Hence, the correct option is c) .