AP calculus BC - differentiation

Question

For all real numbers x, f is a differentiable function such that f(-x) = f(x). Let f(p) = 1 and f'(p) = 5 for some p>0.

1) Find f'(-p)

2) Find f'(0)

3) If l1 and l2 are lines tangent to the graph of f at (-p, 1) and (p, 1), respectively, and if l1 and l2 intersect at point Q, find the x and y coordinates of Q in terms of p

Answer 1

I can help you with part of this. f is an even function like x² or cos x.

f'(-x) = -f'(x)

Since f is even, Rolle's theorem guarantees that f(0)=0

The third part is just a bunch of algebra based on your answer to the first 2 parts.