Solving a Real-Valued Differentiable Function Problem

[ludi_srbin]

Alright, here is the problem.

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

a) Find f'(-p)

b) f'(0)

c) 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 x- and y- coordinates of Q in terms of p.

 

[ludi_srbin]

O yeah I forgot. I got the a) part easily. Others I can't do.

 

[Physics Monkey]

For part b), try using that fact that $$0 = - 0$$ and the properties you should have deduced about the derivative of an even function.

For part c), just construct the two tangent lines. You have enough information to do this if you use the symmetry of the function and its derivative.

 

[ludi_srbin]

Thanks man. I appreciate it.