1.Does a continuous function mean differentiable function ? If a function f(x) is continuous at a number a , then , f(x) has a derivative at a number a.Is it true ? For instance , we know the function f (x)=|x|is continuous at a number 0 , is it true that f(x) has a derivative at a number a ? Example 1 : Where is the function f(x)=|x|differentiable ? Solution : We know if x>0 , then f(x)=|x|=x.And we choose hsmall enough that x+h>0 , hence f(x+h)=x+h=x+h. Therefore , for x>0 , we have If a function f (x) is continuous at a number a, then, f (x) has a derivative at a number a.Is it true? For instance, we know the function f (x) = | x | is continuous at a number 0, is it true that f (x) has a derivative at a number a? Example 1: Where is the function f (x) = | x | differentiable? Solution: We know if x> 0, then f (x) = | x | = x.And we choose hsmall enough that x + h> 0, hence f (x + h) = x + h = x + h. Thus, for x > 0, we have