For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)...

Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2-4x+2

Accepted Answer

Solve for F of X plus H F of X plus H minus F of X and F of X plus H minus F of X over H for the following function X squared minus seven X plus four. Let's first go ahead and find F of extra sausage. What this will mean is everywhere we have an X, well, instead of replace it with X plus H. So we look here, so we have X plus H squared minus seven times X plus H plus four. I want to simplify this X plus A squared. It's gonna expand X squared plus two H X plus eight square. Now, we just should be our seven negative seven X and negative seven H plus four. We can't simplify this anymore. So that is our F F X plus H. Now let's look at the F of X plus H minus F of X. So let's take what we got for F of X S H X squared plus two H X plus eight squared minus seven, X minus seven H plus four and some tract X squared minus seven X plus four. We'll get X squared plus two H X plus H squared minus seven, X minus seven H plus four minus X squared plus seven X minus four. But now cancel some stuff out. We can cancel out. Alright, squared R seven XS and our force That leaves us with two HX plus eight squared minus seven H which cannot be factored as H times two X plus H minus seven. Finally, we want to find F of X plus H minus F of X over H. So take what we got for. Our last answer is divided by H H two X plus H minus seven over H cancel those out. We just get two x plus H -7. We can't simplify this anymore. So if you look at our answers, we can determine the answer to our problem is answered with everyone of our equations here. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2-4x+2

Key Concepts

Function Evaluation

Difference Quotient

Limit Concept

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