Answer to Question #157019 in Calculus for Tom Garland

Question #157019

The derivative of f is x^3(x+5)(x-1). At which values of x will the graph of f have a relative maximum? A relative minimum?

1
Expert's answer
2021-01-21T19:22:07-0500

The graph can have relative minimum or maximum at points 0, - 5, 1. To determine which is which we should find the sign of the derivative of f on corresponding intervals.

1. "f' \\in (-\\infty ;-5) => f'<0 => f" decreases

2. "f' \\in (-5;0) => f' > 0=> f" increases

3. "f' \\in (0;1) => f'<0=>f" decreases

4. "f' \\in (1; \\infty) => f'>0=>f" increases

That means "x=-5" is relative minimum, "x=0" is relative maximum, "x=1" is relative minimum of f.


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