Question

The Mean Value Theorem can be applied to which of the following functions on the closed interval [-5,5]?

A f(x) = 1 sin x
B f(2)= x-1/|x-1|
C f(x) = x²/x²-36
D f(x)= x²/x²-4

Answer 1

The Mean Value Theorem can be applied to a function on the closed interval [-5,5] if it is continuous and differentiable on that interval. Among the given options, only f(x) = 1 sin x satisfies these conditions.

Step-by-step explanation:

The Mean Value Theorem can be applied to a function on the closed interval [-5,5] if the function is continuous on that interval and differentiable on the open interval (-5,5). Let's analyze each option to see if it satisfies these conditions:

1. f(x) = 1 sin x: This function is continuous and differentiable on the interval (-5,5), so the Mean Value Theorem can be applied to it.
2. f(2)= x-1/|x-1|: This is a specific value, not a function. The Mean Value Theorem only applies to functions, so this option does not satisfy the conditions.
3. f(x) = x²/x²-36: This function is undefined for x = ±6, so it is not continuous on the interval [-5,5]. The Mean Value Theorem cannot be applied to it.
4. f(x)= x²/x²-4: This function is undefined for x = ±2, so it is not continuous on the interval [-5,5]. The Mean Value Theorem cannot be applied to it.

Therefore, the only option for which the Mean Value Theorem can be applied on the closed interval [-5,5] is f(x) = 1 sin x.