(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 a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?

Question

(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 a particular commodity that will be produced with K
thousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3
Suppose that capital expenditure varies with time in such a way that t months from now
there will be K(t) thousand dollars of capital expenditure, where
K(t) =2t4 + 3t + 149 / t + 2

(a) What will be the capital expenditure 3 months from now? How many units will be produced
at this time?
(b) At what rate will production be changing with respect to time 5 months from now?
Will production be increasing or decreasing at this time?

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