Calculus/Pre-Cal

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Expert: - 9/30/2011


Question
Good evening. i was trynig to get some help on this problem. Im getting confused.
f(x)=3x^3-15x^2+18x
Find the test interval, representative x value, the value of f, the sign, and the point on the graph. Please help me figure this out, Your help is greatly appreciated! (:

Answer
The interval of usage must be given in the problem.
The x-values are the values in this interval.
The value of f is found by putting in the corresponing value of f.
The sign is determined by whether the graph is positive of negative.

The derivate of f(x) is f'(x) = 3*3x^(3-1) - 2*15*x^(2-1) + 18x^(1-1),
and this gives the slope of the curve.

This can be rewritten as f'(x) = 9x^2 - 30x + 18.
The places where f'(x) = 0 are where the maximum and minimum occur.

This means the maximum of f(x) is between 0 and 1, and the minimum is between 2 and 3.

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