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# P18 - B t and B 00 t Give the units for each At what time(s...

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Project 18 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. Examine the function y = tan( x ) . Calculate d dx y , d 2 dx 2 y and d 3 dx 3 y . Evaluate the first and second and third derivatives at x = 0 . Show that, by coincidence, d 2 dx 2 y = 2 y dy dx = d dx y 2 . Show that this is not generally true, using the function y = e x as a counterexample. Show that d 3 dx 3 y = 2(1 + y 2 )(1 + 3 y 2 ), using the identity 1 + tan 2 ( x ) = sec 2 ( x ) . 1

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2. The population of a bacteria (in thousands) in a certain puddle is given by B ( t ) = 2 + (2 t 2 - 1) e - 2 t where t is the number of days from the present ( t = 0) . Calculate
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Unformatted text preview: B ( t ) and B 00 ( t ). Give the units for each. At what time(s) t is the population experiencing zero growth? (You will need quadratic formula and may round to the nearest tenth.) At what time(s) t is the size of the population experiencing zero acceleration? negative acceleration? As time passes (to inﬁnity), how many bacteria remain? (We haven’t tech-nically learned how to do this yet (L25), but take your best guess if you aren’t sure.) 2...
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