Develop a simple programming code (C/C++/Fortran/Matlab) for calculating the following quantities from a given general rate expression of the form -rA = f(Ca) = k1Ca/(1 + K2Ca^2) or kCa(Co-Ca) as an example, which has a non-monotonically increasing or decreasing trend, i.e. an autocatalytic reaction: (a) derivative at a point, (b) area under the curve, (c) finding a minimum or maximum functional value over the given domain, (d) drawing a straight line (with an equation y = mx + c) between two points on the function, and (e) searching for a point where the tangent is the same as the given slope.