does anyone know how to do this calculus problem?

Question

Let p and q be real numbers and let f be the function defined by:

f(x) = 1+2p(x-1)+(x-1)^2 for x
= qx + p for x>1

a) find the value of q, in terms of p, for which f is continuous at x=1
b) find the values of p and q for which f is differentiable at x=1

thanks for the help!

Answer 1

for x=1 f(x) = 1 + 0 + 0 = 1
and lim x -> 1 qx + p = q+p

thus f is continuous in x=1 when p+q=1

2) for differnetiable , the left and right hand side limit should be equal, I am sure you can solve this now by yourself.

left hand limit is 2p and the rihgt handlimit is q so 2p = q