Determine if the function f(x)=44−x2√ satisfies the mean value theorem on [0, 2]. if so, find all numbers c on the interval that satisfy the theorem.

The function f(x) satisfies the Mean Value Theorem

Step-by-step explanation:

Mean Value Theorem states that if f be a function such that,

Then there is at least a number c in (a, b) such that,

Here, the given function,

∵ f(x) is defined for all real values x for which 44-x² ≥ 0

44 ≥ x² ⇒ ±√44 ≥ x ⇒-√44 ≤ x ≤ √44

Thus, f(x) is continuous on [0, 2],

∵ f'(x) is defined for all values on the interval (0, 2),

Thus, f(x) is differentiable on (0, 2),

Now,

Hence, the function f(x) satisfies the Mean Value Theorem

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

step-by-step explanation: