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Critical points

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Please help with attached problems #2 and #10
thanks

Find the intervals on which f is increasing or decreasing. Find the local maximum and minimum values of f. Find the intervals of concavity and inflection points.

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Solution Summary

This provides an example of finding concavity, inflection points, maximum and minimum values, and using the first and second derivative tests.

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Let f (x) = x^4 - 4x - 1 ; then f ' (x) = 4(x - 1)(x^2 + x + 1) in which case x= 1 is the only critical point, and is a local minimum. This means the graph is decreasing for x < 1 and increasing for x > 1. There are ...

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