Search code examples
rcurvealgebra

R find the x and y value where the curve changes sharply

I have a dataset with two columns x, y as follows

  x           y
  0.5789474   0.0011382324
  1.0000000   0.0024540588
  0.8000000   0.0017039382
  0.7272727   0.0014921618
  0.8421053   0.0018399977
  0.8611111   0.0019049152
  0.3750000   0.0007843210
  0.7837838   0.0016542579
  0.7222222   0.0014784711
  0.7619048   0.0015895130
  0.7435897   0.0015372644
  0.4375000   0.0008791528
  0.8750000   0.0019537960
  0.6666667   0.0013359048
  0.8750000   0.0019537960
  0.8571429   0.0018911749
  0.6896552   0.0013931524
  1.0000000   0.0024540588
  0.9285714   0.0021543502
  0.9523810   0.0022499579

Plotting these values produces a graph as follows

enter image description here

My goal is to find the values of x and y where the slope or rate of change in the curve is maximum. Where the bend or curve is sharpest. I tried ,

(lead(y)-y)/(lead(x)-x) and this is did not work. Any suggestions or advice is much appreciated. Thanks in advance.

Solution

  • I am giving pointer:

    df = read.table(text=" 
   0.5789474   0.0011382324
   1.0000000   0.0024540588
   0.8000000   0.0017039382
   0.7272727   0.0014921618
   0.8421053   0.0018399977
   0.8611111   0.0019049152
   0.3750000   0.0007843210
   0.7837838   0.0016542579
   0.7222222   0.0014784711
   0.7619048   0.0015895130
   0.7435897   0.0015372644
   0.4375000   0.0008791528
   0.8750000   0.0019537960
   0.6666667   0.0013359048
   0.8750000   0.0019537960
   0.8571429   0.0018911749
   0.6896552   0.0013931524
   1.0000000   0.0024540588
   0.9285714   0.0021543502
   0.9523810   0.0022499579",header=FALSE)

    Now calculate slope:

    slope= diff(df$V2)/diff(df$V1)

    From the maximum slope retrieve the corresponding x,y points:

    df[which.max(slope),]

    Output:

        V1          V2
 18  1 0.002454059

    Please feel free to correct me!