Question about finding where the function increases and decreases on f ( x ) =...

Izabelle Lowery

Izabelle Lowery

Answered

2022-10-20

Question about finding where the function increases and decreases on f ( x ) = 1 x .
f ( x ) = 1 x , x 1
I have been staring at this equation for a bit. Things I'm confused on.
the derivative of this is: f ( x ) = 1 x 2 now, how am I supposed to find where this derivative increases/decreases? Do I find the critical points first? by setting the derivative to 0? or do I solve it like 1 x 2 > 0 cross multiply to make it: 1 > x 2 and if so once I square this does it make the result x = 1 , x = 1? I'm really lost here and it seems like it should be easier.
Does setting the derivative to > or < or = and solving for the x give a critical point?

Answer & Explanation

Rene Jordan

Rene Jordan

Expert

2022-10-21Added 10 answers

Explanation:
Recall that intervals of increase and decrease of f correspond to intervals of positivity and negativity of f′, and critical points of f are where the roots of f′ are. Try graphing the function 1 x 2 using software. Where is the function positive, where is it negative, and where are its roots (if it has any)?

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