The function defined below satisfies rolles theorem on the

Question

1. The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (-3, 0) where f'(c)=0.

f(x) = x³ + 6x² + 9x, [-3, 0].

2. The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (-4, -2)where f'(c)=0.

f(x) = x + 8x^-1 , [-4, -2].

3. The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval (1, 2) where f'(c)=(f(b) - f(a))/(b - a).

f(x) = x³ - 1.5x , [1, 2].

4.The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval (1, 2) where f'(c)=(f(b) - f(a))/(b - a).

f(x) = 1.1x^-1 + 1.6 , [1, 2].