is x^(1/5) defined and continuous in that interval?
(-1)^(1/5) = -1 etc, seems ok
how about arc cos x
that looks fine
x/(x-3) woukld blow up at x = 3, but we do not go there so it is ok
but
Oh my, sqrt(-1) is imaginary! and is called i for want of a real number to use. It is a no, no
Which of the following functions does not satisfy the conditions of the Mean Value Theorem on the interval [-1, 1]?
a. 5th root of x
b. 2x arccosx
c. x/(x - 3)
d. sqrt(x + 1)
2 answers
a is ok, since it is differentiable on (-1,1). It has a vertical tangent, bot only at the endpoint(s).
b is ok for the same reason
c is ok
d is real on the interval, since it's √(x+1), so it's ok too
Looks to me like they all work, since the MVT requires
1. f(x) is defined and continuous on the interval [a,b]
2. differentiable on (a,b)
b is ok for the same reason
c is ok
d is real on the interval, since it's √(x+1), so it's ok too
Looks to me like they all work, since the MVT requires
1. f(x) is defined and continuous on the interval [a,b]
2. differentiable on (a,b)