 In this video, we will present the solution to question number nine for practice exam number two for math 12 10 We are given the limit as h approaches 0 of 1 plus h to the 10th minus 1 over h And we're told that it represents the derivative of some function f at some number a and we're supposed to identify What the function f and the number a must be now this requires? We know the definition of the derivative which it really comes in two forms So the first form that we're going to use very often the f prime of x is the limit as h approaches 0 of f of x plus h minus f of x all Over h like so and in particular since we're looking for a specific number not the general function necessarily What we can do is we can erase the variable x right and Instead we use the specific number a You'll see that right there That's the first form the other version of the derivative that could come into play right here Is you'll see something like the limit as b approaches a of f of b minus f of a Over b minus a For which that could be a b this looks really like the slope formula But that symbol b could be anything it wants to be right it doesn't actually have to be a b It's just a placeholder just a slider just much like over here doesn't have to be an h Although that's the symbol we use most often you could have like the limit as x approaches a of f of x minus f of a over x minus a Those two versions are both appropriate in this one now looking at the limit as h approaches 0 We have this h in the bottom it tells us that this is the format that we are going to be using here So we should see that then this right here should then be f of of a plus h and Then this right here Should be f of a Well given that this function right here is f of a plus h I see a one plus h that makes me think that hmm Maybe a plus h is equal to one plus h that is to say a equals one Well, if that's the case, what's then the function in play well The a plus h seems to be sitting inside of the power function f of x equals x to the tenth Notice if I take one plus h and I put it inside of this function right here You'll get one plus h to the tenth so that seems to check out here Let's then also test my hypothesis if f is x to the tenth and a is equal to one What is then f of one that'll be one to the tenth? One to the tenth which is then equal to one which is exactly what that number is right here So that that gives us what we're looking for We're looking for x is the tenth power and a equals one which that then gives us as The correct answer B