7. Find the equations for the tangents to the graphs of the following functions at the specified points: x2 - 1 (a) y = 3- x-x2 atx = 1 ( b ) y = at x = 1 x2 + 1 (c) y = (72+1) (x2-1) atx = 2 *+1 (d) y = at x = 0 ( * 2 + 1 ) ( x + 3 )8. Consider an oil well where x(t) denotes the rate of extraction in barrels per day and p(t) denotes the price in dollars per barrel, both at time t. Then R(t) = p(t)x(t) is the revenue in dollars per day. Find an expression for R(t), and give it an economic interpretation in the case when p(t) and x(t) are both increasing (Hint: R(t) increases for two reasons.)- SM 9. Differentiate the following functions w.r.t. t: at + b (a) ( b ) In ( avt + b ) (c) ct + d at2 + bt + c