General question on polynomial sketching (2 Viewers)

[sadpwner]

How do you determine how steep a turning point will be without calculous? Say given y=(x-2)(x-1)(x-3)^2(x-5)^2. The curve between 2 < x < 3
will be closer to the x-axis. What is the general behaviour of the curve near the T.Ps? I only determined that the curve near the first multiplicity that is greater than 1 from the left hand side is closer to the x-axis, it is smaller the higher power is and if it is of multiplicity 1 then it is steeper the further it is from the next x-intercept.

 

[seventhroot]

You dont need to be 100% accurate with your sketches afaik

 

[sadpwner]

it could matter if i am sketching 2 graphs on the same axis

 

[braintic]

it could matter if i am sketching 2 graphs on the same axis

If you really want to get it that accurate, just sub in some values.