Jim Whitney

Economics 102

 Limits, slopes and derivatives  The "delta" (D) method  

General procedure	Example: Y = X2
Step1: Start with an initial value of X and Y:    Y = (f(X))
Step2: Choose a nearby value for X:    X' = X+DX
Step3: Compute the nearby value for Y:    Y' = f(X+DX)
Step4: Compute the slope formula:    DY    f(X+DX) - f(X)    f(X+DX)-f(X)    --- = --------------- = -------------   DX     (X+DX) - X           DX
Step5: Compute the derivative:    dY          DY          f(X+DX)-f(X)    -- =  LIM  ---- =  LIM  ------------    dX   DX->0 DX    DX->0     DX

 
In the diagram, ch = "delta", and X^2 = X squared.