Given f(x) = -1/x, find all c in the interval [-3, -½] that satisfies the Mean Value Theorem.
A. c= -sqrt(3/2)
B. c= +or- sqrt(3/2)
C. The Mean Value Theorem doesn’t apply because f is not continuous at x=0
D. The Mean Value Theorem doesn’t apply because f(-½) does not equal f(-3)
E. none of these
3 answers
I think I got it. Is it B?
f' = 1/x^2
at x = -3, f = 1/3
at x = -1/2, f = 2
slope = (2 - 1/3)/(-1/2 + 3)
= (5/3)/(5/2) = 2/3
where is the derivative = 2/3 ?
1/x^2 = 2/3
x^2 = 3/2
x = +/- sqrt (3/2)
yes B
at x = -3, f = 1/3
at x = -1/2, f = 2
slope = (2 - 1/3)/(-1/2 + 3)
= (5/3)/(5/2) = 2/3
where is the derivative = 2/3 ?
1/x^2 = 2/3
x^2 = 3/2
x = +/- sqrt (3/2)
yes B
I believe the answer is (A), given the interval [-3,-½]
4 answers