Calculus

1. Determine whether Rolle's Theorem applied to the function f(x)=((x-6)(x+4))/(x+7)^2 on the closed interval[-4,6]. If Rolle's Theorem can be applied, find all numbers of c in the open interval (-4,6) such that f'(c)=0.
2. Determine whether the Mean Value Theorem applied to the function f(x)=x^2 on the closed interval[4,12]. If Mean Value Theorem can be applied, find all numbers of c in the open interval (4,12) such that f'(c)= f(12)-f(4)/(12-4).
3. Determine whether the Mean Value Theorem applied to the function f(x)=2sinx+sin2x on the closed interval[4pi,5pi]. If Mean Value Theorem can be applied, find all numbers of c in the open interval (4pi,5pi) such that f'(c)= f(5pi)-f(4pi)/(5pi-4pi).

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