Can we use the mean value theorem to say that the equation f prime of x is equal to negative one has a solution, and now the interval is from zero to two. If so, write a justification. All right, so let's see this. So if we were to take the slope of the secant line, so f of two minus f of zero, all that over two minus zero, this is equal to negative two minus zero. All of that over two, which is equal to negative two over two, which is equal to negative one. And so, and we also know that we meet the continuity and differentiability conditions. And so we could say, and since f is generally differentiable, generally differentiable, differentiable, it will be differentiable, differentiable, and continuous over the interval from zero to two.