I'm trying to show that there are an infinite number of functions that minimize the integral: $$\int_0^2[(y')^2*(1 + y')^2] dx$$ subject to $y(0) = 1$ and $y(2) = 0$.
(They are continuous functions with piecewise continuous first derivatives.)
I'm trying to show that there are an infinite number of functions that minimize the integral: $$\int_0^2[(y')^2*(1 + y')^2] dx$$ subject to $y(0) = 1$ and $y(2) = 0$.
(They are continuous functions with piecewise continuous first derivatives.)
Consider the two lines given by the graphs of
$$
f(x)=1-x
\\
g(x)=2-x
$$
Now pick $0