f:= x -> sqrt(x)-3*x^3+1;
dfdx:= x -> (1/2)*x^(-1/2)-9*x^2;
plot([f(x),dfdx(x)], x=0..2, color=[black,red]);
plot([f(x),dfdx(x)], x=0.. .1, y=1..1.3, color=[black,red]);
F:= x -> x^(3/2)/(3/2)-3*x^4/4+x;
plot([f(x),F(x)], x=0..2, color=[black,red]);
plot([x^2-2*x+3, 2*x-2], x=-3..3, color=[black,red]);
plot([x^3-5/x^2+2, 3*x^2+10*x^(-3)], x=-4..4, y=-40..40, color=[black,red]);
plot([2*x^Pi+x^(-42)-17*x,2*Pi*x^(Pi-1)-42*x^(-43)-17], x=0..3, y=-50..50, color=[black,red]);
plot([7/x-x+4, -7*x^(-2)-1], x=-3..3, y=-10..10, color=[black,red]);