tangentplane.jl

# Julia
begin
	using  Plots;
	
	plotly()

	transparent_red = RGBA(200/255,60/255,60/255,200/255)
	transparent_gray = RGBA(30/255,30/255,30/255,230/255)
	
	abc(x,y) = 4x^2+4x*y+y^2+2x+5y+3

	x_range = range(-10,stop=10,length=100)
	
	surface(
		x_range,
		x_range,
		abc,
		color = transparent_red,
		label = "f(x,y)",
		legend = :none
	)
	
	surface!(
		x_range,
		x_range,
		(x,y) -> -18x-5y-22,
		color = transparent_gray,
		label = "t(x,y)"
	)
	
	plot!(
		[-3], [1], [27], 
		color=:blue, 
		marker=:circle, 
		markersize=2, 
		label = "point"
	)
end