And so, and since f is generally differentiable, it will be differentiable and continuous over zero, two. So the mean value theorem tells us, tells us, that there is an x in that interval from zero to two such that f prime of x is equal to that secant slope, or you could say that average rate of change is equal to negative one. And so I could write yes, yes, and then this would be my justification. This is the slope of the secant line or the average rate of change. And since f is generally differentiable, it will be differentiable and continuous over the closed interval. So the mean value theorem tells us that there is an x in this interval such that f prime of x is equal to negative one. And we're done.