chemical engineering

Develop a simple programming code (C/C++/Fortran/Matlab) - for calculating the following quantities from a given general rate expression of the form r(A)=f(Ca)=k1Ca/(1+K(2)Ca2) or kCa(CoCa) 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, etc