SOLUTION: Determine whether the Mean Value theorem can be applied to f on the closed interval f(x) = sqrt2-x, [−7, 2] If the Mean Value Theorem can be applied, find all values of

Question 1187614: Determine whether the Mean Value theorem can be applied to f on the closed interval
f(x) = sqrt2-x, [−7, 2]
If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b)such that f '(c) = f(b) − f(a)/b − a. (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
You determine whether it satisfies the hypotheses by determining whether
is continuous on the interval [,] and differentiable on the interval (,). (Those are the hypotheses of the Mean Value Theorem)
You find the mentioned in the conclusion of the theorem by solving
'
' on the interval (,).
f is continuous on its domain, which includes [,]

' exists for all so it exists for all in (,)
Therefore this function satisfies the hypotheses of the Mean Value Theorem on this interval.
To find solve the equation
' ... ,
'
discard any solutions outside (,), and you get

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