Problem : 1) f (x) = x ² - 4x on [2, 4]

Solution for Problem 1 >>

f'(c)	=	= 2
2c - 4	=	2
c	=	3

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Problem : 2) f (x) = sin(x) + cos(x) on [0, 4Π]

Solution for Problem 2 >>

		f'(c) = = 0
		cos(x) - sin(x) = 0
		x = ,,, or

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Problem : 3) f (x) = on [1, 2]

Solution for Problem 3 >>

f'(c)		=
		= -
-		= -
c		= ±

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Problem : 4) On the interval [-5,5], there is no point at which the derivative of f (x) =|x| is equal to zero, even though f (- 5) = f (5) . Is this a contradiction of Rolle's theorem?

Problem : Find the number c that satisfies Rolle's theorem for f (x) = sin(x) on the interval [0, Π] .

Solution for Problem 5 >>

(sin(x))' = cos(x)
cos(x) = 0 at x =

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