Question

integral test question

Answer 1

for series I know that in order to perform an integral test it must satisfy three condtions. f(x) must be greater then or equal to zero. f(x) must be continuos along a given interval. and f(x) must be decreasing.

Answer 2

the problem I have is condtion three. I know for OBVIOUS examples like 1/n2 etc . BUt for thew ones that are not as obvious you take the first derivative right? but after you take the first derivative how would you be able to tell is decreasing?

Answer 3

@freckles

Answer 4

A function that is always decreasing will have a negative derivative.

Answer 5

It will always be negative.

Answer 6

so how would you test for it to be negative? @wio

Answer 7

It needs to always be negative.

Answer 8

For example, \(-x\) will always be negative when you know \(x>0\).

Answer 9

ohh ok thank you