Given f(x)=4+3/x find all values of c in the interval (1,3) that satisfy the mean value theorem.

A. 2
B. Sqrt(2)
C. Sqrt(3)
D. +or- sqrt(3)
E. MVT doesn't apply

I got C

1 answer

Hmm...
Mean value says that
(f(x2)-f(x1))/(x2-x1) = f(x0)
where x0∈[x1,x2]
(f(x2)-f(x1))/(x2-x1) = (5-7)/2 = -1

f'(x)=-3/x^2
f'(sqrt(3))=-3/3=-1,

Yes, C is correct.