Increasing/Decreasing Intervals of y=|2-x| and x/(x^2)-1

[parwana]

On what intervals is y= l 2-x l increasing or decreasing?? Wouldnt it be its always increasing cause of the absolute symbol, but that's not the answer.

Also find where x/(x^2) - 1 is increasing/decreasing??

Given tan(xy)= x^2, find y'

y' of (sinx)^x

 

[humanino]

I am concern about the fact the answer to our first question is really obvious, but your two last ones are not so easy. If somebody asked you to tackle non-linear differential equations, you should be able to solve absolute value problems for a while now.

 

[Muzza]

Whether or not a function is positive has nothing to do with it being increasing or decreasing. Draw a graph of |2 - x|. Surely the answer will come to you.

For the other function, study the sign of its derivative.

 

[Shahil]

Uh..shouldn't this be in the homework forum??

Anyway - if my memory serves me correctly, the y = |2-x| is a "V" shaped graph - that should help you with the visualisation. I'm sure you'll figure out the rest of the problem once you draw the graph.

 

[JonF]

#1 Maybe it would help you if you broke it into an inequality

y= l 2-x l is equivalent to

if x > 2 then y= -1*(2-x)
if x < 2 then y = 2-x


for #2 where is that functions critical points? i.e. where does it’s derivative = 0. Then in what intervals of the critical points is the derivative positive?


#3 Given tan(xy)= x^2, find y'

Ill give you a hint the derivative of the left is

The derivative of tan(xy) multiplied by the quantity x’y + y’x

This is implicit differentiation so you will need to solve for y’


#4 y' of (sinx)^x

If y = (sinx)^x
This is chain rule.
The outer most function is g(x) = k^x and the inner function is k(x) = sinx