How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for $f(x) = (x - 1)/x$ ?

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How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for $f(x) = (x - 1)/x$ ?

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Answer 1 · 2015-12-23T18:54:22

You need its derivative in order to know that.

Explanation:

If we want to know everything about $f$ , we need $f'$ .

Here, $f'(x) = (x-x+1)/x^2 = 1/x^2$ . This function is always strictly positive on $RR$ without $0$ so your function is strictly increasing on $]-oo,0[$ and strictly growing on $]0,+oo[$ .

It does have a minima on $]-oo,0[$ , it's $1$ (even though it doesn't reach this value) and it has a maxima on $]0,+oo[$ , it's also $1$ .

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How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for $f(x) = (x - 1)/x$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for f(x) = (x - 1)/xf(x) = (x - 1)/x?

1 Answer

Explanation:

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Impact of this question

How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for $f(x) = (x - 1)/x$ ?