1. The left-hand and right-hand derivatives of () = ₀^- (+)()/ and + () = 0⁺ (+)() / if these limits exist. Then () derivatives exist and are equal.

a) (4) and + (4) for the function () = { 0 0

{ 5 0 < < 4 <--- (All of them in the same {})

{ / () if x 4

b) Sketch the graph of .

c) ?

d) Where is ?

2) Find an equation of the tangent line to the curve = ⁴ + 1 to the line 32 = 15.

3) The normal line to a curve C at a point P is the line through P that is perpendicular to the tangent line at P. Find an equation of the normal line to the curve = to the line 2 + = 1.

4a) For what values of x is the function () = |² 9| differentiable? Find a formula for .

b)

I would really appreciate if someone helps me with this. My professor gave us a lesson on derivatives and gave us a handout that is completely different than what he explained.