Simplify the difference quotient ƒ(x+h)-ƒ(x)/h

Question

ƒ(x) = 4x-3

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says for the function F of X is equal to 17 X minus 15, calculate the simplified form of the difference quotient, which is the quantity of F of X plus H minus F of X in quantity divided by H. We're given 4 possible choices as our answers. For choice A, we have 17 H. for choice B, we have 17 divided by H. For choice C, we have 17. For choice D, we have 17 X divided by H. So we're asked to calculate the simplified form of the difference quotient, which is the quantity of F of X plus H. Minus F of X in quantity divided by H. So, all we need to do is use our function F of X that we're given the problem to calculate this quotient. So, our difference quotient is going to be equal to or F of X plus H, I'll just substitute in for X X plus H into our function F of X. And so I'm going to get 17, multiplying the quantity of X plus H in quantity minus 15. They don't have minus F of X, so that's gonna be the quantity of 17 X minus 15. In quantity, and all this is divided by H. So we can actually simplify the numerator. And so this is going to be equal to, we'll distribute the 17 into the quantity of X plus H. we'll have 17 X. Plus 17 minus 15. And then we'll distribute the minus sign into the 17 X minus 15. So we'll have minus 17 X. Plus 15 and all of this is still divided by H. We can continue to simplify our numerator. And we noticed that we have 17 X minus 17 X, so that's going to add to zero, so those two terms will cancel out. We have minus 15 plus 15, so when to add those two, they will add to 0. And so what I'm left with on the numerator is going to be 17H. And that is divided by H. And so the Hs will cancel out, and so our difference quotient is going to be equal to 17. So this is the answer that I was looking for. And if I look over at my answer choices, the correct answer choice corresponds to answer choice C. So, I hope that this explanation has been useful, and I'll see you in the next video.

Simplify the difference quotient ƒ(x+h)-ƒ(x)/h
ƒ(x) = 4x-3

Key Concepts

Difference Quotient

Function Evaluation

Algebraic Simplification

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