verify that g(x)=3x sqrt(x-5) satisfies the condition of rolle's theorem on the interval [0,5]. Find all numbers c that satisfies rolles theorem.

Answer 1

g(0) is not defined, since sqrt(-5) is not real.

So, g(x) does not satisfy the condition that g(0) = 0

You want to reconsider any part of the question?

Answer 2

Sorry +5

Answer 3

In that case,
g(0) = 0
g(5) = 15√10

Again Rolle's Theorem does not apply. Try again.

Answer 4

I think you want

g(x) = 3x√(x+5) on [-5,0]

g(-5) = 0
g(0) = 0

So, we want c somewhere in (-5,0) such that f'(c) = 0

f'(x) = 3(3x+10) / 2√(x+5)
f' = 0 when 3x+10 = 0
So, c = -10/3 which is in the domain.