y
Therefore
dA
dt  = dx
dy
y
x
dt
dt
⋅
+
⋅
= – 3(6) + 10(2)
(as x = 10 cm and y = 6 cm)
= 2 cm2/min
Rationalised 2023-24
 MATHEMATICS
150
Example 5 The total cost C(x) in Rupees, associated with the production of x units of
an item is given by
C(x) = 0 005 x3 – 0 02 x2 + 30x + 5000
Find the marginal cost when 3 units are produced, where by marginal cost we
mean the instantaneous rate of change of total cost at any level of output Solution Since marginal cost is the rate of change of total cost with respect to the
output, we have
Marginal
cost (MC) =
0