3. Consider the function p(x) = (2x³ − 4x + 3)⁰. A. If f(x) = 2x³ - 4x + 3 and g(x) = x6, then function p is equal to exactly one of the following: fog or go f. Which is it? Explain. B. Thinking of function p as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for p'(x). C. Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of f, simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.

3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d %3D dx |x| b) Sketch the graphs of the function f(x) = |x| and its derivative. %3D c) Use the result of part (a) to differentiate the function g(x) = x|x|. Write the derivative as a simplified monomial. %3D

Note: (a) and (b) are not asking the same thing. :-) 5. For the function y = f(x), graphed below, answer the following questions. (a) Find f(2) y 8- (b) Find f(5) 6 5. 4. (c) Find the net change of f(x) from x-2 to x=5. 3- 2- 1- 0. 4 6. 7 8. (d) Fill in the blanks. There will be many possible correct answers. The net change of f(x) will be a negative number from x to x= 6. State the domain of each of the following functions in interval notation. Function Domain f(x) = x-5 g(x) = &x + 3 h(x) = Vx +7

Find the points on the graph of f (x) = + x -a 1 where the slope is 2. %3D O (1, 2/3) O (0,-1) and (-2, 7/3) O (1.-2/3) and (-3,2) O (1,2/3) and (3,2)