Find the slope of the following curve and X = 6. So we're going to find the slope of any location, and then we're going to stick in the six. So we're going to do the limit as H approaches 0 of 1 / X + H - 4 - 1 / X -, 4 all over H Now recall that this is really just our limit as H goes to 0 of F of X + H -, F of X all over H formula. So from here we're going to get a common denominator. I'm going to multiply this one by X - H or X - 4 / X - 4 and I'm going to multiply this other one by X + H - 4 over X + H - 4. So when we do that, we get X - 4 minus the quantity X + H - 4 if we distribute that negative through negative X -, H + 4, so X and negative X cancel -4 and +4 cancel. And this divide by H is the same thing as multiplying by 1 / H or the H stays in the denominator. So this H on top in the numerator and the H in the denominator are going to reduce, leaving us just a -1 placeholder in the top. So we get -1 / X + H - 4 * X - 4. The limit is H goes to 0. So now we're actually going to stick zero and for H and we're going to get -1 / X - 4 * X - 4 or X - 4 ^2. So then when we look at what happens at the location of X = 6, we're going to take this equation, put in six 6 -, 4 two 2 ^2 4, so negative 1/4.