please help answer and show steps! thank you so much :)

6. (a) (4 points) Find the equation of the line that is tangent to y = 8 2:4 at a: = 1. (b) (2 points) Use your answer from the previous part to approximate 8 (1.01)4 7. (6 points) Determine the positive real numbers a: and y such that o :1: + y = 4 and o 2:132 + y2 is as small as possible. 3 63:2 + 9:1: . 8. (4 points) Suppose that f (IE) is a function such that f'(3:) : LPT5~. Flnd the interval(s) on which f (as) is increasing. 9. (6 points) Consider the following information about the graph of a continuous function m(:r): o limr_,_00 m(.r) 2 2 and limHoo m(:1:) = 2 o The table below summarizes when m' and m\" are positive and negative, but with some information unknown: -2