Making Sure the Graphs I Plot is Correct

Hi all,

I just want to make sure that the graphs plot I made are correct. It is a limit problems in Calculus. I am just doubting if the graphs of mine are correct.

I want t know whether we can automatically plot the:

  1. Saddle point
  2. all local and global maximum or minimum point when the first derivative is zero
  3. The measurement of x axis and y axis, instead of 0,1,2,... can we make it into smaller increments like, 0,0.02,0.04,...?

Can the package of GR or Pyplot or anything plot it automatically? like scatter! function

using Plots, LaTeXStrings

f(x) = abs(x-1)/(x-1)
g(x) = abs(x-1)/(x-1)
h(x) = (x^2 - abs(x-1) - 1)/abs(x-1)
i(x) = (1/(x-1))-(1/abs(x-1))

p1 = plot(f, -8, 8)
p2 = plot(g, -8, 8)
p3 = plot(h, -8, 8)
p4 = plot(i, -8, 8)

l1 = L"\lim_{x \rightarrow 1} \frac{|x-1|}{x-1}"
l2 = L"\lim_{x \rightarrow 1^-} \frac{|x-1|}{x-1}"
l3 = L"\lim_{x \rightarrow 1^-} \frac{x^2 - |x-1| - 1}{|x-1|}"
l4 = L"\lim_{x \rightarrow 1^-} \frac{1}{x-1}-\frac{1}{|x-1|}"

plot(p1, p2, p3, p4, layout = (2, 2), xaxis = "x", yaxis = "y", label="", legend=:outertop,
title=[l1 l2 l3 l4],
titleloc = :bottom, titlefont = font(8))

On (3) you can just do xticks = -9:0.2:9.

(1) and (2) aren’t really questions for a plotting package, but for packages which implement methods to find saddle points or extrema - just have a google around or search this forum to find discussions like

thanks for the answer, it helps a lot