Secant Lines

Some secant lines through (h,f(h)) and (0, f(0)) as h approaches zero from the right.

> gseclines(cos(x),x=0,right);

Secant line through (h,f(h)) and (0, f(0)) as h approaches zero from the right is pictured in red The secant as h approaches zero from the left is pictured in blue.

> gseclines(cos(x),x=0);

Here is a piecewise defined expression.

> f:=piecewise(x<=1,2-x^2,x>1,x^2);

> gseclines(f,x=1);

Do you think that this function has a derivative at x = 1?

>