[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)?
Then, also using the Racetrack Principle, what quadratic function h(t) can we prove is greater than than f(t) (for t>=0)?
I have NO clue!