please answer all and show work! thank you so much :)

6. (a) (4 points) Find the equation of the line that is tangent to y = 8 - x* at x = 1. (b) (2 points) Use your answer from the previous part to approximate 8 - (1.01)4 3 7. (6 points) Determine the positive real numbers x and y such that . xty = 4 and . 2x2 + y is as small as possible. 8. (4 points) Suppose that f(x) is a function such that f'(x) = 25 - 6x2 + 9x Find 202 + 5 the interval(s) on which f(x) is increasing. 9. (6 points) Consider the following information about the graph of a continuous function m(x): . lime-- m(x) = -2 and lim,-. m(x) = 2 . The table below summarizes when m' and m" are positive and negative, but with some information unknown: x