Can someone provide a function that satisfies all of the following:

Question

• p(−1) = 3 and lim x→−1 p(x) = 2
• p(0) = 1 and p'(0) = 0
• lim x→1 p(x) = p(1) and p'(1) does not exist

Thanks!

Answer 1

I first thought of x^2+1, but f(-1) = 2.
So, next, 2x^2+1

f(x) =
x^2+1 for x in (-5,-1)U(-1,1)
3 for x = -1
2 for x > 1

I think this fits the bill.