Still confused as to how I incorporate f(x) = f(x+1)
I have that between (0 , g(0)) and (1, -g(0)) there has to be a coordinate (x , 0), but then how do I get from that back to f(x) = f(x+1)?
Wow I'm a bit stuck today. I'm just going around and around in circles with:
g(0) = f(0) - f(1)
g(1) = f(1) - f(2)
I juggle them around and end up with:
f(0) - g(0) = g(1) + f(2)
f(1) - f(2) = f(1) - f(0)
which brings me nowhere.
Homework Statement
Find the derivative of:
[SIZE="4"]\frac{(x^{3} + 5x^{2} − 9x + 4)^{3/4}}{(x^{4} − x^{3} + x^{2} − x + 1)([x^{5} − x^{-5}]^{1/2})}
Homework Equations
Product Rule
Quotient Rule
The Attempt at a Solution
I've attempted using the quotient rule for the entire thing...
Homework Statement
Suppose that f(x) is a continuous function on [0,2] with f(0) = f(2). Show that
there is a value of x in [0,1] such that f(x) = f(x+1).
Homework Equations
Intermediate Value Theorem?
Extreme Value Theorem?
Periodicity?
The Attempt at a Solution
For sure there's an...