Absolute maximum and minimum values
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1. Given f(x) = x [(x+3)^1/2]
a) Find the intervals on which f is increasing and decreasing.
b) Find any relative extrema that f may have.
c) Find the intervals of concavity and inflection points of f.
d) Sketch the graph of f.
2. find the absolute maximum and minimum values of f(x) = ln(x^2 + x + 1) on the interval [-1, 1].
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Solution Summary
Absolute maximum and minimum values
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1. First we graph f(x) (see attachment).
Next, we compute the first and second derivatives of f, which we should have
f' = (3(x+2))/(2sqrt(x+3)) and f'' = (3(x+4))/(4(x+3)^(3/2))
a) to find where f is increasing, we want its first derivative to be positive. f' ...
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