how to increase function values through its derivetive

we have a derivetive funtion df/dx .

i want to manipulate df/dx in a way to increase the values of the original function f(x) ,

in which way (or many ways if exists) should i move df/dx values in pupose to increase f(x) values .?

this is the graphe of the derivative df/dx throught x.

contexte: the increase of the f(x) throught its derivetive will serve me at the end to increase.

integral of f(x) along x.

Answer 1

[Star Strider]

Do some simple experiments to see what produces the desired result —

syms k x 
dx1 = 2*x;                                      % Original Derivative
Idx1 = int(dx1)                                 % Original Function

Idx1 = 

dx2 = k*dx1;
Idx2 = int(dx2)                                 % Multiplies Original Function

Idx2 = 

dx3 = k + dx1;
Idx3 = expand(int(dx3))                         % Introduces Trend (Slope) Plus Offset To Original Function

Idx3 = 

Experiment with variations on these (Symbolic Math Toolbox required here) to determine what works best.

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