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F(x)=-(x-5)^3
F'(x) = -3(x-5)^2
F''(x) = (-3)(2)(x-5)
F''(x) = -6(x-5)=0

x=5 is a point of inflection

Test for concavity:
Consider the intervals (-8 ,5), (5, 8)

choose any one point from each of the intervals.
if F''(x) < 0 , F(x) is concave down on that interval
if F''(x) > 0 , F(x) is concave up on that interval

F''(x)= -6(x-5)
(-8 ,5): choose x=1; F''(1)=24 > 0, f is concave up on (-8 ,5):
(5, 8): choose x=6; F''(1)=-6 < 0, f is concave down on (5, 8):

F is concave up on (-8 ,5):

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Home >All Categories > Science & Mathematics >Mathematics >Open Question Becky Boo Member since:March 28, 2011Total points:85 (Level 1)an airline is interested in determining the average number of unoccupied seats for all of its flights. It selects an SRS of 81 flights and determines that the average number of unoccupied seats for the sample is 12.5 seats with a sample standard deviation of 3.9 seats.
a. construct a 95% confidence interval for the true number of unoccupied seats for all flights.
b. interpret your confidence interval in context of the problem.Answer Question

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Home >All Categories > Science & Mathematics >Mathematics >Open Question Danzer Member since:March 08, 2011Total points:89 (Level 1)In an air pollution study performed at an experiment station, the following amounts of suspended benzene-soluble organic matter (in micrograms per cubic meter) were obtained for eight different samples of air: 2.2, 1.8, 3.1, 2.0, 2.4, 2.0, 2.1 and1.2. Assuming that the population is normal, construct a 95% confidence interval for the corresponding true mean.Answer Question

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