WB2.1 - Rates of Change and Tangent/Normal Lines

Is it possible to find the tangent line of the function at a x=0:

f(x)=\begin{cases} -x, & x<0 \\ x^2-x, &x \geq 0 \end{cases}

If yes, find it. If no, explain why not.

Is it possible to find the tangent line of the function at a x=2:

f(x)=\begin{cases} -x, & x<0 \\ x^2-x, &x \geq 0 \end{cases}

If yes, find it. If no, explain why not.

Find the tangent line of f(x) at x=-3 for f(x)=x^{2} - 4x.

Find the normal line of f(x) at x=4 for f(x)=x^{2}-4x.

Find the secant line of f(x) over the interval [-1,2] for f(x)=x^{2}-4x.

Find the normal line of g(t) at t=0 of g(t)=2t^{2}-5.

Find the secant line of k(w) at w=3 of k(w)=4w^{2}-3w.

Find the tangent and normal slopes of f(x) at x=4 of f(x)=3x^{2}-9 and the secant slope of f(x) over the interal [-3,1].