In this problem, we will cover the velocity of a function. So to solve the first part of this problem, we know that we want to find the derivative when T. of zero is equal to one. So I'm going to write F prime or not every time S prime of one and we know that it's going to equal the limit. S. T Approaches one of S and t Minour as of one over c minus one. And we know what S. And P. Is. And when we plug in one for S and T, we will get to so we have the square root of four T -2 Over T -1. And in order to get rid of that square root on the top, we will multiply the top and the bottom By the Square root of 14 plus two. And what that gives us is limit as T approaches one, So we get 40 -4 On top, And then T -1 Times the square root of 40 plus two on the bottom. And we see that we could factor the top. So let me write the limit as he approaches one. We can pull out four in front and right T -1, And this is going to be over T -1 Times the square root of 4ty plus two, And we can cancel out the T -1. So we will be left with the limit as t approaches one of four over the square root of 14 plus two, and if we were to plug in one for thi We would be left with four over four, which ultimately becomes not to think one and that is our velocity. And so for the second part Of the problem we will do the same thing. We want to find the derivative when T0 is equal to four. So I'll write as prime four equals the limit. As T approaches for Of S. A. G- S. A. four. All over t minus four. And we already know what S. And P. Is. And when we plug in four for tea we will get four. So the top should be the square root of 4ty minus four Over T -4. And to rationalize this will multiply the job and the bottom by the square root of 40 plus four, same for the bottom. And that yields us the limit as T approaches four of 40 minus 16. This is going to be over t minus four Times the square root of 4ty plus four. And we see that we can factor the top. We can take out of four from both 40 and 16, So we will have four times t minus four All over to you -4 Times The Square Root 40 Plus four. These cancel out, and we are left with the limit as T approaches for of four over the square root of 40 plus four. And when we plug in 440 we will get that are derivatives is going to be four over eight, which can be simplified to one half.