Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=\dfrac12x^2 -10xd(x)= 2 1 x 2 −10xd, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, x, squared, minus, 10, x How many seconds after diving will Rui reach his lowest altitude?
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Given : Rui is a professional deep water free diver. His altitude (in meters relative to sea level), d(x) = (1/2)x² - 10x
To find : How many seconds after diving will Rui reach his lowest altitude
Solution:
d(x) = (1/2)x² - 10x
d'(x) = x - 10
putting d'(x) = 0
=> x - 10 = 0
=> x = 10
d''(x) = 1
=> d(x) has minimum value when x = 10
d(x) = (1/2)x² - 10x
d(10) = (1/2)10² - 10(10)
= 50 - 100
= -50
After 10 Seconds of diving Rui reach his lowest altitude = - 50
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Answer:
10 seconds
Step-by-step explanation:
50m
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