Are the endpoints included in an interval where they ask for the interval for which a function is increasing? The endpoints in the case mean that the derivative is equal to zero. Are those included in the interval or not?
any help please?
Yes they are man. (1,0) means numbers inbetween 1,0 but not itself, however, [1,0] means 1 0 and the numbers inbetween
But that can’t be right. They aren’t increasing on {1,0}, bc the slope on the endpoints are zero
“Increasing” means for any two points the function of a larger value is larger. It’s not defined in a single point. The derivative value is used to prove that the function is increasing, but it’s not involved in a definition (in fact, an increasing function doesn’t need to have a derivative). So yes, if for any point in the interval the function value is larger that the value at the left endpoint, this endpoint is included, and similarly with the right endpoint. This would be the case if the derivative is positive everywhere except the endpoints.