Suppose (x^2-1)/x^2+3)on the interval [-3, 3]. Use Rolle’s Theorem, if it applies, to find all values c in the open interval (-3, 3) such that f'(c) = 0.

c = -3.5

c = 0

c = 3

Rolle’s Theorem does not apply

Question

Suppose (x^2-1)/x^2+3)on the interval [-3, 3]. Use Rolle’s Theorem, if it applies, to find all values c in the open interval (-3, 3) such that f'(c) = 0. 

c = -3.5
		
c = 0
		
c = 3
		
Rolle’s Theorem does not apply

anonymous · Answer

f is continuous and differentiable on [a,b], and f(a) = f(b), rolle's theorem guarantees there exists a number c in (a,b) such that f'(c) = 0

so, set f'(x) = 0 and solve for x

anonymous · Answer

ok so the derivative is 8x/(x^2+3)^2

then what?????

anonymous · Answer

set it equal to 0

anonymous · Answer

so do i solve the top for zero or bottom?

anonymous · Answer

which which do you think?

anonymous · Answer

top???? cause the bottom would make it undefined???

anonymous · Answer

That's true, though you the denominator in this case will never be 0.

anonymous · Answer

so the answer of the problem is 0???!!!

anonymous · Answer

bingo

anonymous · Answer

YAY!!!! thanks so much for helping me figure it out on my own!!!!

anonymous · Answer

yw