Differentiability of three types of functions with absolute value
By using the definition of derivative and the principle of mathematical induction,the differentiability of three kinds of functions with absolute values is discussed.It is proven that(1)If y=f(x)is derivable at the point x0,then the differentiability of v=|f(x)| at poinx0 depends on f(x0)and f'(x0);(2)For any positive integer k,y=(x-a)k |x-a| has a k order derivative at the point a,and no k+1 order derivative;(3)If g(x)is continuous at the point a,then the differentiability of y=|x-a| g(x)at point a depends on g(a).
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维普
