11DIFFERENTIATION - Department of Mathematics

FIGURE T1
The graph of f in the viewing window
[0, 7] [0, 12]
Exercises
c. The graph is shown in Figure T1.
In Exercises 1–8, find the value of the second
derivative of f at the given value of x. Express
your answer correct to four decimal places.
1. f(x) 2x 3 3x 2 1; x 1
2. f(x) 2.5x 5 3x 3 1.5x 4; x 2.1
3. f(x) 2.1x 3.1 4.2x 1.7 4.2; x 1.4
4. f(x) 1.7x 4.2 3.2x 1.3 4.2x 3.2; x 2.2
5. f(x) x2 2x 5
x3 ; x 2.1
1
6. f(x) x3 x 2
2x 2 ; x 1.2
5x 4
7. f(x) x1/2 2x 3/2 1
2x 1/2 ; x 0.5
3
x 1
8. f(x) ; x 2.3
2x x 4
9. R ATE OF B ANK F AILURES The Federal Deposit Insurance
Corporation (FDIC) estimates that the rate at which
757
banks were failing between 1982 and 1994 is given by
f(t) 0.063447t 4 1.953283t 3 14.632576t 2
6.684704t 47.458874 (0 t 12)
where f(t) is measured in the number of banks per year
and t is measured in years, with t 0 corresponding to
the beginning of 1982. Compute f (6) and interpret your
results.
Source: Federal Deposit Insurance Corporation
10. M ULTIMEDIA S ALES According to the Electronic Industries
Association, sales in the multimedia market (hardware
and software) are expected to be
S(t) 0.0094t 4 0.1204t 3 0.0868t 2
0.0195t 3.3325 (0 t 10)
where S(t) is measured in billions of dollars and t is
measured in years, with t 0 corresponding to 1990.
Compute S(7) and interpret your results.
Source: Electronics Industries Association