Calculus/Calculus

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Expert: - 7/25/2011


Question
What are local maximum and minimum values and what does it mean when a question asks for a period if applicable for a function? For example a function like y=(x+2)/(x^(2)-6x+5)

Answer
The maximum and minimum values are where the derivative is 0.
For this problem, we have y = f(x)/g(x), so y' = (g(x)f'(x) - f(x)g'(x)]/g²(x).
Since f(x) = x+2, f'(x) = 1; since g(x) = x²-6x+5, g'(x)=2x-6.

To find the critical points, find where the numerator is 0 by multiplying everything out.

To fiind the areas where the function is not applicable, that would be where g(x) = 0.
Note that g(x) = (x-5)(x+1), so the points where the function has no value are x=5 and x=-1.

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