Question

7) f(x) = (6e2x - x)3 8) f(x) = eX + 1 ex_1 Solve the problem. 9) The sales in thousands of a new type of product are given by S(t) = 30 - 80e-0.8t, where t represents time in years. Find the rate of change of sales at the time when t = 8. 10) A company's total cost, in millions of dollars, is given by C(t) = 120 - 80e-t where t = time in years. Find the marginal cost when t = 2. 2

Answer 1

f61)-(6- f'(x) = a (662_x)' [u(x)"]=nugh 'u'(x) = 3(602* 3. d. (662x) da Cean) = aeax -36 (227) film = 3(6e-13 (124**-) 8) f(x) et1 e²-1 hom f'(x) = drext da (= uv-uvi 12. 11 (ei) re 1) -(e)le (ep-113 (9-1) (*)-(+1)* (ex-1)2. ex - e2 - en 11 eu f'(x) = -2e² (ex-1) 2.

5 (8) = 648-0-8(8) a ) SH) - 30 -80 -0.8t. 0.8t s'le) = (30-800 50-80 (-0-82-06) s' (t) = 646-0.8t. Rate of change of sales when t=8 years s'(8) = 648 6:4 s'(8) x 0.10634 this and per year. $(8) ~ 10634 Rate of change of sales at t=8 is 0-10634 thousands year (Oy) 1063.4 per year. 10) CH) = 120-80et marginal cost, c'(t) = (120-80et) =0-80 (-e-t) c'(t) = 800 t. when t=2 c'(2) = 8002 Q10.83 marginal cost when t=2 is 10-83 million dollars per year.