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);