math

posted by Eric

Katrina is studying the effect of foreign substances on bacteria populations. If she introduces a
beneficial substance, such as food, the bacteria population grows. If she introduces a harmful substance,
such as a poison, the bacteria population decreases. The function
f(x) = x4 - 20x3 + 141x2 - 414x+ 432, where x is the time in days, models the bacteria population rate of growth or decrease over time. Determine when the bacteria's population was
increasing.

b) Describe the bacteria population between days 3 and 6. Explain what positive, negative, and values of 0
mean in this situation.

1. Steve

f(x) increasing when f'(x) > 0
f'(x) = 4x^3 - 60x^2 + 282x - 414
= 2(x-3)(2x^2-24x+69)
The roots are 3,6±√(3/2) = 3.00,4.78,7.22
So, f' > 0 in (3,6-√(3/2) U (6+√(3/2),∞)

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