So this right over here, this is the graph of y is equal to f of x. We're saying that the slope of the secant line, or our average rate of change over the interval from a to b, is our change in, is our change in y, our change in y, that the Greek letter delta is just shorthand for change in y over our change in x. Over our change in x, which of course is equal to this. And the mean value theorem tells us that there exists, so if we know these two things about the function, then there exists, there exists some, some x value in between a and b. So in the open interval between a and b, there exists some c, there exists some c, and we could say it's a member of the open interval between a and b, between a and b. Or we could say some c such that a is less than, such that a is less than c, which is less than b. So some c in this interval.