Please help with all parts. Thanks and will give rating!

3. Find the value of o. and of b for which the line 2:1: + y = b is tangent to the function f(:r) = 0.11:2 at 3: = 2. 4. Suppose f (:12) measures the population of Mexico, in millions of people, where a: is the number of years since 1980. (a) What are the units of f'(:r)? (1)) Explain, in context, the meaning of f'{6) = 2. ((3) Explain, in context, the meaning of f(_1](95) = 16. _ d 1 _ ~ '2 (d) What are the units of dz: (f (113)) . 32:2 + 1 if :1: a (a) Show that a = 1 and a. = 1 are the only values for which lim f (2:) exists. (b) Use the denition of continuity to nd all values of a. and b that make f (3:) a continuous function