How can I differentiate modulus?

[ojsimon]

Ok so i was wondering if what i am doing is correct, But it gets the wrong minimum point?
So my function is y=|x+4|

1) y^2=x+4
2)2y(dy/dx)=1
3)dy/dx = 1/2y
4)dy/dx = 1/2|x+4|

I set that 0 and get
0=1/(2(|x+4|))

Am i write in thinking this cannot be solved? or missing something?

Thanks

 

[Mentallic]

Yep that's right. It's the same as asking what number x can be used to make 1/x=0? None of course. And at x=-4 the derivative is undefined.

 

[Cyosis]

It goes wrong from the start, y^2 \neq x+4.

 

[Mentallic]

Oh right, I guess I brushed over it too fast.

When that mistake is fixed, you'll still find the the derivative cannot equal zero anywhere and it's still undefined at x=-4 with the form 0/0

 

[ojsimon]

Oh yeah, thanks,

 

[Mark44]

Another approach is to get rid of the absolute values by writing the function as
y = x + 4, x >= -4
y = -(x + 4), x < -4

Then y' = 1 for x > -4 and y' = -1 for x < - 4. y' does not exist at x = -4.

Any extreme points of a function occur at places where y' = 0, or y' is undefined, or at finite endpoints of the domain in cases where a function is defined only on an interval [a, b].