Question

I need a function of x that is equal to zero at x = -1 and x = 1, also it needs to be decreasing on (-infinity, -1)U(-1,1) and increasing on (1, infinity)

Answer 1

If it's decreasing between -1 and 1 how can it take the same values there?

Answer 2

what?

Answer 3

Yeah. By Rolle's Theorem, there should a number between -1 and 1 where the derivative is 0.

Answer 4

you said f(-1)=0 and f(1)=0. And also that the function is decreasing on (-1,1)

Answer 5

gerr sorry change increasing, decreasing to posative, negative

Answer 6

positive*

Answer 7

53

zzr0ck3r
I need a function of x that is equal to zero at x = -1 and x = 1, also it needs to be negative on (-infinity, -1)U(-1,1) and positive on (1, infinity)

Answer 8

sorry about that

Answer 9

That means -1 is a double root so that a candidate for the function is \(\large f(x)=(x+1)^2(x-1).\)

Answer 10

thank you

Answer 11

No prob.