Is ( 1,-1) a solution to the following system of inequalities:
1 answer:
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Answer:
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,
- It is continuous on [a, b].
- It is differentiable on (a, b).
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