(i) Find the rate of change of the function f(x) = (x + 2)/( 1 ?8x) with respect to x when x = 1. (ii) The number of units Q of aparticular commodity that will be produced with K thousand dollarsof capital expenditure is modeled by Q(K) = 500 K ^(2/3). Supposethat capital expenditure varies with time in such a way that tmonths from now there will be K(t) thousand dollars of capitalexpenditure,where K(t) = (2t^4 + 3t + 149)/( t + 2) (a) What willbe the capital expenditure 3 months from now? How many units willbe produced at this time? (b) At what rate will production bechanging with respect to time 5 months from now? Will production beincreasing or decreasing at this time?
