1)Form a polynomial that is at least 4 th degree. Use your polynomial to find/demonstrate each of the following:

a) Find all of the critical numbers of your polynomial

b) Identify the interval(s) over which your function is increasing and decreasing.

c) Identify the coordinates (? and ?) of any extrema (maximums and minimums)

d) Identify the interval(s) over which your function is concave up and concave down. Your function must exhibit both characteristics at least once.

e) Identify the coordinates (? and ?), of any inflection points

2) Form and answer a question that asks to find the derivative of an implicitly defined equation. Your question must also include either the product or quotient of two functions as well. These two functions must have different variable names. In other words, your solution must incorporate implicit differentiation AND either the product rule or quotient rule.

3) Form and answer a question that asks to find the slope of a line tangent to an explicitly defined curve at a given point. This task is a bit more difficult than may seem as you need to make sure that the point that you choose is on the curve that you define.