Why Is the Derivative of e^|x| Undefined at x=0?

[takercena]

Homework Statement

a)How to differentiate fx=e^|x|?
b)Why when x = 0, f'(x) is undefined

Homework Equations

The Attempt at a Solution

Is it d/dx e^|x| = e^|x|? I have no idea for this question.

 

[Dick]

|x|=x if x>=0 and |x|=(-x) if x<0. Split the problem into those two cases. To find out what happens AT x=0 look at the limits from both sides.

 

[takercena]

So there are two answer right? -1/e^x and e^x. Why f'x is undefined at x = 0?

 

[takercena]

Hello, please i still don't get it. I sketch 2 graph from the equation and at x = 0, there is a line there. But why f'(x) for e^|x| is undefined when x = 0?

 

[tiny-tim]

Hello, please i still don't get it. I sketch 2 graph from the equation and at x = 0, there is a line there. But why f'(x) for e^|x| is undefined when x = 0?

Hi takercena!

Your sketch shows two graphs, reflections of each other, joined together …

do they join smoothly, or with a corner?

 

[Dick]

So there are two answer right? -1/e^x and e^x. Why f'x is undefined at x = 0?

There aren't really two answers, it just that the formula for the answer looks different for x>0 than it does for x<0. If x is close to 0 and negative f'(x)~(-1), if positive then f'(x)~1. There's a sharp corner on the graph of f(x) at x=0, just like on |x|. So f(x) doesn't have a well defined slope there.

 

[takercena]

Oh i see. Thanks