Question

Show that the function is not the derivative of any function on the interval -1<=x<=1

Answer 1

F(x)= 0, -1<=x<=0. And 1, 0<=x<=1

Answer 2

Hello

Answer 3

You must understand that derivative= slope-of-tangent-line

Answer 4

Hello....okay

Answer 5

BUT if a graph is to have a tangent it MUST, MUST MUST be without jumps or discontinuities (however this is NOT sufficient)

Answer 6

Your example is undergoing a jump - so no tangent is possible - neccessary for smoothness is at LEAST CONTINUITY !

Answer 7

You have a Stair-like graph - draw it !

Answer 8

So i get that much but how do I show that the function is not the derivative?

Answer 9

Oh sorry - the argument is as follows:

Answer 10

- You Assumption says that the function from which the "stair" is the derivative must have DERIVATIVE IN ALL THE POINTS OF [-1,1]

Answer 11

But Derivative - means , well-defined value of the derivative , whch is EQUAL from both "sides " of the point

Answer 12

However at point 0 - you do NOT have a well defined single value of the derivative - you have 2 one-sided limits which are NOT equall,. Which means derivative Does NOT exist at 0

Answer 13

The one-sided limits must be equal

Answer 14

So how do I SHOW that? Cause I understand tht It fails at 0 but I don't know how to show tht