Example plots for this ask.sagemath question:
f = x^3; xmin = -1; xmax = 1; small=.001;
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P = plot(f, (x, xmin, xmax),legend_label="$x^3$");
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P + arrow((xmin, f(x=xmin)),(xmin-small,f(x=xmin-small)))\
+ arrow((xmax, f(x=xmax)),(xmax+small,f(x=xmax+small)))
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f = cos(x^2); xmin = -1; xmax = 1; small=.001;
P = plot(f, (x, xmin, xmax),legend_label="$cos(x^2)$");
P + arrow((xmin, f(x=xmin)),(xmin-small,f(x=xmin-small)))\
+ arrow((xmax, f(x=xmax)),(xmax+small,f(x=xmax+small)))
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var("x y")
f = x^2+y^3-2; xmin = -2; xmax = 2; small=.01;
fd = f.derivative(x)/f.derivative(y); fd
2/3*x/y^2 2/3*x/y^2 |
ymin = find_root(f(x=xmin),-2,2); ymax = find_root(f(x=xmax),-2,2);
print ymin, ymax
print fd(x=xmin,y=ymin), fd(x=xmax,y=ymax)
-1.25992104989 -1.25992104989 -0.83994736659658209 0.83994736659658209 -1.25992104989 -1.25992104989 -0.83994736659658209 0.83994736659658209 |
P = implicit_plot(f, (x,xmin,xmax), (y,-2,2), legend_label="$x^2+y^3-2=0$")
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(P + arrow((xmin, ymin),(xmin-small,ymin+small*fd(x=xmin,y=ymin))) \
+ arrow((xmax, ymax),(xmax+small,ymax-small*fd(x=xmax,y=ymax))) \
).show(aspect_ratio=1)
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