Question

Help drawing graph with derivatives and conditions!

Answer 1

At least they give you all those points, instead of finding them.

start by drawing the plane, and plotting those first 4 points on it

Answer 2

So the first one I know is all the x intercepts so it looks something like:

Answer 3

[except that dot is supposed to be more towards 3 than 2 xD

Answer 4

meh... the general shape is what is important

Answer 5

th esecond bullet tells you where the first derivative is zero, a tangent here will be horizontal

Answer 6

plot those points, and remember the function may change from increasing to decreasing or other way around at these points

Answer 7

Right, under those instructions it also has
a) Determine the values for x at which all local maximums and minimums occur. Justify.
b) Determine the values of x at which all points of inflection occur. Justify.
c) Give a sketch of the graph

idk if those are helpful in finding the graph? should I do those first?

Answer 8

How do I plot those derivative points? o.0 just put those points on the x axis as well?

Answer 9

right, we can move on for now, just keep in mind the function may change direction at those x values from increasing to decreasing

Answer 10

or decreasing to increasing

Answer 11

the limit as x goes off to infinities can tell you if there is a horizontal asmytpte, here they give you 2 of them