Right, out of all the tangent lines of a function on a interval which one is the minimum area between the function and a tangent line.
I'm looking for a proof to prove this:
The minimum area between x^2, and its tangent line on the interval [0,1] is the tangent line evaluated at x=1/2
How would you write a proof that proves that the minimum area between a function and its tangent line is the tangent line evaluated at point p, where p is the midpoint on a given interval?
i.e. The minimum area between x^2, and its tangent line on the interval [0,1]...