11DIFFERENTIATION - Department of Mathematics

Exercises
In Exercises 1–6, use the numerical derivative
operation of a graphing utility to find the rate
of change of f(x) at the given value of x. Give
your answer accurate to four decimal places.
1. f(x) (2x 2 1)(x 3 3x 4); x 0.5
2. f(x) (x 1)(2x 2 x 3); x 1.5
x 1
3. f(x) ; x 3
x 1
4. f(x) x(x2 4)
x3 ; x 4
1
5. f(x) x(1 x1 )
; x 1
x 1
6. f(x) x2 (2 x)
; x 1
1 x
7. N EW C ONSTRUCTION J OBS The president of a major housing
construction company claims that the number of construc-
b. Using the numerical derivative operation of a graphing utility, we find
f(0) 57.5266
f(2) 14.6165
c. The results of part (b) show that the treatment benefit drops off at the
rate of 58% per hour at the time when the heart attack first occurs and falls
off at the rate of 15% per hour when the time to treatment is 2 hours. Thus,
it is extremely urgent that a patient suffering a heart attack receive medical
attention as soon as possible.
tion jobs created in the next t months is given by
f(t) 1.427t2 140t 700
3t 2 80t 550
where f(t) is measured in millions of jobs per year. At
what rate will construction jobs be created 1 yr from now,
assuming her projection is correct?
8. P OPULATION G ROWTH Amajor corporation is building a
4325-acre complex of homes, offices, stores, schools, and
churches in the rural community of Glen Cove. As a result
of this development, the planners have estimated that
Glen Cove’s population (in thousands) t yr from now will
be given by
P(t) 25t2 125t 200
t 2 5t 40
a. What will be the population 10 yr from now?
b. At what rate will the population be increasing 10 yr
from now?
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