How do you know a function is increasing?

1 Answer
Noah G
Mar 9, 2018

It will be increasing when the first derivative is positive.

Explanation:

Take the example of the function #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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Hopefully this helps!

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