Question

15) The cost of producing x units of a commodity per week is C(x) = 0.2x3 - 18x2 + 32x +200 Find all values of x where C"(x) - 0. How are these levels of production related to the graph of the marginal cost? A) X= 3. It corresponds to a maximum on the graph of C'(x). B) x - 30. It corresponds to a point of inflection on the graph of C'(x). C)x= 30. It corresponds to a minimum on the graph of C '(x). Dx = 3. It corresponds to a minimum on the graph of C(x).

Answer 1

C) 0.2x3-18 x2 +322x200 now: for c'(x)=0 we need to find out: C" (X) = d2 Cox) da? वर da - dla CCM)) el comoda e re (0-2x3-1842 +324 +200) c'w= 0.602 -36x +32 CCX)= (0.642-30% +32) an Chce 1:24-36 = 0 a- 36 - 360 -[30 1.2 so if the second derivative is equal to kero ; that mean that point is corresponding to infleetich point so: b) 2=30; correspond to inflection of graph of c'(a).