If f+g is differentiable, then are f and g differentiable too?

[samer88]

Homework Statement

if f and g are two continuous functions and f+g is differentiable...are f and g differentiable? if not give a counter example!

Homework Equations

The Attempt at a Solution

 

[clementc]

I'm thinking not necessarily, but I'm not really sure. Whether a function is differentiable or not depends on whether on not every point on it has a derivative.

So say f is y = x^(1/3), and g is y = -x^(1/3). Both f and g are continuous - the graph of the function is unbroken.

(Technically the definition of continuity is that for every value in the domain the limit from below = limit from above = the value itself but yeah that's not really important.)

f+g is differentiate yeah? f + g just gives y = 0
However, y = x^(1/3) and y = -x^(1/3) are both non differentiable, since at the origin x = 0, the derivative is undefined. You get a divide by zero from memory =P

 

[samer88]

thnx clementc

 

[clementc]

haha no worries! =P