So it's going to be derivative of t with respect to t is one. Derivative of two t to the negative two, let's see, negative two times positive two is negative four t to the, and we just decremented the exponent here, t to the negative negative three power. Now, to find acceleration as a function of time, we just take the derivative of this with respect to time. So acceleration as a function of time is equal to, actually since I've already used that color for the average, let me do a different color now. So acceleration as a function of time is just the derivative of this with respect to t. So derivative of a constant with respect to time, well, it's not changing, so it's a zero, and then over here, negative three times negative four is positive 12 times t to the, let's decrement that exponent, to the negative four power. Now, to find the average value, all we have to do now, average value, is essentially take the definite integral of this over the interval and divide that by the width of the interval. So, or we could say, we could take, we could divide by the width of the interval, one over two minus one, and this all simplifies to one, times the definite integral over the interval.