[SOLVED] Racetrack Problems

PLEASE HELP ASAP!!!!!!!!!!

1). Consider the functions f(x)=lnx and g(x)=x−1. These are continuous and differentiable for x>0. In this problem we use the Racetrack Principle to show that one of these functions is greater than the other.

(a) Find a point c such that f(c)=g(c). c=???

(b) Find the equation of the tangent line to f(x)=lnx at x=c for the value of c that you found in (a).

For part a, I thought the answer was c=1, but that's not correct.

2). Suppose that f(t) is continuous and twice-differentiable for t>=0. Further suppose f''(t)<=9 for all t>=0 and f(0)=f'(0)=0.

Using the Racetrack Principle, what linear function g(t) can we prove is greater than than f(t) (for t>=0)?

g(t)= ???

Then, also using the Racetrack Principle, what quadratic function h(t) can we prove is greater than than f(t) (for t>=0)?

h(t)= ???

I have NO clue!