Page 58 - How To Solve Word Problems In Calculus
P. 58
(b) ρ(x) = m (x) = 12x 2
ρ(2.5) = 75 slugs/ft
6. Boyle’s law may be stated PV = C . Since P = 80 when V = 40,
C = 80 · 40 = 3200.
PV = 3200
3200
P =
V
= 3200V −1
dP −2
=−3200V
dV
3200
=− 2
V
dP 3200
2
When V = 20, =− =−8 lb/in per in 3
dV 20 2
7. Since revenue = (number of items sold)(price per item),
2
R(x) = (500 − 2x − 0.1x )x
2
= 500x − 2x − 0.1x 3
R (x) = 500 − 4x − 0.3x 2
R (10) = 500 − 40 − 30
= 430
The marginal revenue derived from the sale of the 11th unit is $430.
45
