 In this video, we provide the solution to question number eight for practice exam one for math 1050 We're given the function f of x equals x squared plus 3 and we're asked to compute the arbitrary change of said function f on the interval negative 1 to 4 now remember to find the average rate change the delta y over delta x Again evaluated from negative 1 to 4 We're going to use the formula where we have to take f of 4 Minus f of let me scooch over a little bit f of negative 1 and Then we do this over 4 minus negative 1 do notice on the bottom You got a negative negative so that is in fact going to be a positive number in the end So you end up with a 4 plus 1 down below So we have to evaluate f at 4 and a negative 1 right there So if we plug these in there, you're going to end up with a 4 squared plus 3 Minus a negative 1 squared plus 3 Be cautious on your parentheses right there Notice in the top. I mean I actually could have a plus 3 and a minus 2 those actually cancel out So I'm actually going to simplify and use that result for us going forward in the denominator the 4 plus 1 is a 5 So in the numerator coming back, we have the square of the 4 which is 16 We're then going to subtract from it negative 1 squared negative 1 squared by order of operations is actually going to be a positive 1 So we get 16 minus 1 which is a 15 divide that by 5 that gives us 3 And so we see that the average rate of change is choice D