Page 221 - How To Solve Word Problems In Calculus

Since P(x) = R(x) − C(x),

MP(x) = MR(x) − MC(x)

MP(10) = MR(10) − MC(10)
= 9.00 − 7.00

= $2.00

By definition of the derivative of C(x),

MC(x) = C (x)

C(x + h) − C(x)
= lim
h→0 h
C(x + h) − C(x)
≈ if h is small in comparison to x.
h
If h = 1

MC(x) ≈ C(x + 1) − C(x)

Thus the marginal cost approximates the additional cost in-
curred in producing one additional item. Similarly,

MR(x) ≈ R(x + 1) − R(x)

and

MP(x) ≈ P(x + 1) − P(x)

EXAMPLE 6

The cost of manufacturing x baseballs is
2
C(x) = 0.05x + 0.5x + 50. How much will it cost to produce
the 101st baseball? Find the exact value and compare with the
approximate value using marginal cost.

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