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,
(e) searching for a point where the tangent is the same as the given slope, etc.

Develop computer code to determine the required minimum volume of different reactor systems for treating an organic containing effluent the inputs are:
Flow rate of the wastewater = 0.05-0.2 m3/min
Concentration of the organics in wastewater = 1-20 mmol/m3
Required concentration in the treated stream = 0.1-2 mmol/m3

System:

1. a single pfr
2. a single CSTR
3. two stirred tank of any size
4. a combination of pfr and mfr
5. a pfr with recycle

Computer code should also be able to determine the rate of the reaction from the following measurements used to study the degradation of the organics in the wastewater samples using a laboratory scale. MFR:
Ca (inlet) = 1-25 mmol/m3
Ca (exit) = 0.1-5 mmol/m3
Tau(min) = 50-1