Posted by laila on Tuesday, March 26, 2013 at 11:00pm.
find the following for the function f(x)=(x+5)^2(x2)^2
a.find the x and y intercepts,
b.find the power function that the graph ressembles for large values of x c.determine the maximum number of turning points on the graph of f
d.determine the behavior of the graph of f near each xintercept
I don't even know where to begin. please help.

math pre calculus  Steve, Wednesday, March 27, 2013 at 11:38am
surely the intercepts are easy
f(x) is a polynomial of degree 4, so for large x it just looks like x^4.
Since the graph just touches the xaxis at x=5 and 2, It comes down from the upper left, touches at x=5, goes back up and comes back down to touch at x=2, then heads on up to the right, it has 3 turning points.
Visit wolframalpha.com and enter
(x+5)^2(x2)^2
to see the graph. It will help clarify the concepts, I think.
Enter
plot y=(x+5)^2(x2)^2 and y=x^4 where 10<x<10
to see how the two graphs are similar for large x.
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