So any non-constant function does not have a derivative that is zero everywhere this is the same as saying that the only functions with zero derivative are the constant functions. #d/dx f(x)/g(x) = \frac#, and again the only point in which this function has no sense is #x=-2#. The Mean Value Theorem tells us that at some point c, f ( c) ( f ( b) f ( a)) / ( b a) 0. These conditions are easily checked, since the only point in which the function is not defined is #x=-2# (since in that point the denominator equals zero), and of course #-2 \notin #.Īs for the derivative, using the ratio formula The mean value theorem requires a function to be continuous in a closed interval #, and differentiable in the open interval #(a, b)#.
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