5) Tangent Lines
Given the function f(x)
> f:=x->x^4/4+x^3/3-x^2+1;
The slope at any point is given by
> m:=x->D(f)(x);
At the point x=2 the slope of the tangent line is
> m(2);
The equation of the tangent line at x=2 is given by
> y:=m(2)*(x-2)+f(2);
We can plot both curves
> plot({y,f(x)},x=-3..3,-5..5);
Maple has a package called student
> with(student);
> showtangent(f(x),x=2,x=-3..3,-5..5);