How do you know a function is increasing?

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How do you know a function is increasing?

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Answer 1 · 2018-03-09T05:39:15

It will be increasing when the first derivative is positive.

Explanation:

Take the example of the function $f (x) = e^{x^{2} - 1}$ $f(x) = e^(x^2 - 1)$ .

The first derivative is given by $f'(x) = 2xe^(x^2 - 1)$ (chain rule). We see that the derivative will go from increasing to decreasing or vice versa when $f'(x) = 0$ , or when $x= 0$ .

Whenever you have a positive value of $x$ , the derivative will be positive, therefore the function will be increasing on ${x|x> 0, x in RR}$ .

The graph confirms

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How do you know a function is increasing?

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Explanation:

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