Please explain all steps in detail from your own work for good feedback.

4. The graphs of differentiable functions are continuous and smooth, with defined finite slopes. a) Draw the graph of a function on a coordinate plane. Make sure it is an original drawing-a curve containing at least two bends. Then draw the graph of its derivative function. Explain in words what the second graph reveals about the first one. b) Can a function be differentiable over a domain and not be continuous over that domain? Can a function be continuous over a domain and not be differentiable over that domain? Explain. c) Name three different reasons a function may be nondifferentiable at a particular point. 5. Shown at right is the circle x + y? = 3. The trigonometric operations are defined as follows. (x, y) cos 0 = - sin 0 = 2 tan d = x seco = - csc 0 = - cot 8 = - a) Draw a picture similar to the one drawn here. Instead of an unknown radius r, use a radius of one. Show cose, sin 0 , tan 0 , sec , csco, and cot 0 as distances on your picture. To accomplish this, you will need to add some lines. If you have drawn it correctly, you should be able to easily visualize the three Pythagorean identities. sin2 0 + cos2 0 = 1 tan- 0 + 1 = sec2 0 cot- 0 + 1 = csc2 0 b) Use your knowledge of the derivatives of sin x and cos x, along with any number of derivative shortcut rules, to demonstrate the derivatives of tan x, secx, csc x, and cot x. c) For each of the three identities shown in part a, differentiate both sides with respect to o and simplify. If differentiated correctly, each of the resulting equations should be obviously true