How can I differentiate modulus?

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SUMMARY

The discussion focuses on differentiating the function y=|x+4| and identifying its critical points. The initial approach using y^2=x+4 is incorrect, leading to an undefined derivative at x=-4. The correct method involves rewriting the function without absolute values, resulting in y' = 1 for x > -4 and y' = -1 for x < -4, confirming that the derivative does not equal zero and is undefined at x=-4. Thus, the function has no minimum points.

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ojsimon
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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
 
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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.
 
It goes wrong from the start, y^2 \neq x+4.
 
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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
 
Oh yeah, thanks,
 
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].
 

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