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@ganeshie8 i think is does because of definition

i understant that but if you include a,b nothing is bad i thing,, it's more correct

|dw:1436725268121:dw|

oh i see now,but sometimes you can include

I think you can include if the function is continuous in the closed interval

yeah it's true

we base whether the function is increasing or decreasing base on what's derivative does

the function's derivative does not exist at x=1 or x=3

instead of "does not exist"

increasing/decreasing is not defined in terms of derivatives; \(f:(a,b)\to\mathbb{R}\) is increasing on \((a,b)\) iff \(x0\implies f(y)-f(x)\ge 0\) or in other words \(x

so basing your understanding of increasing on the existence of derivatives is a bad idea