Question

-/20 POINTS LARAPCALC10 3.5.008. MY Find the number of units x that produces the minimum average cost per unit C in the given equation. C = 0.06x + 58x2 + 1465 units Submit Answer

Answer 1

(1)C(x)= 0.06x® +58x* +1465 <(x) = C(x) = 0.06x° +58x2 +1465 - 405 = 0.06x2 +58x + 1465 C'(x) = 0.06(2x) +58(1) +1465( = 0.127 +58-1485 To find the minimumavearge cost, C'(x) = 0 0.12x +58 – 1465 = 0 x = 5,-5.05227,-483 281 C(5) = 0.06(5)2 +58(5) + 2465 = 584.5 The minimum average cost per unit is approximately 5 units. (2) F(x) = 149 – 32 $'(x)=)23 (-28) 3'(x)= way Therefore, the critical points are x = -7,0,7. Test at x = -1 -(-1) -1=0.1433 1149-(-1) 148=. since the slope is positive it increases. Test at x = 1 F "(1)= =-0.1433 since the slope is negative it decreases. Test at x = -8 148 F'(-8)=-_-(-8) 8 149-(-8)7. -25 Test at x = 8 899 Hizmet Therefore, the function is increasing in the interval (-7,0) and the function decreases in the interval (0,7).