Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Given f (x) = x2 + 5x + 6, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?

Sagot :

facundo3141592

We want to get the difference quotient for the given function, we will get see that the difference quotient is equal to:

f'(x) = 2x + 5

The difference quotient:

For a given function f(x), we define the difference quotient as:

[tex]\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]

In this case, we have:

f(x) = x^2 + 5x + 6

Replacing that in the difference quotient we get:

[tex]\lim_{h \to 0} \frac{(x + h)^2 + 5*(x + h) + 6 - x^2 - 5x - 6}{h}\\\\\lim_{h \to 0} \frac{x^2 + 2xh + h^2 + 5*x + 5*h + 6 - x^2 - 5x - 6}{h}\\\\\lim_{h \to 0} \frac{ 2xh + h^2 + 5*h }{h}\\[/tex]

Now we can cancel the factor h to get:

[tex]\lim_{h \to 0} 2x + h + 5 = 2x + 0 + 5 = 2x + 5[/tex]

So the difference quotient is equal to 2x + 5.

If you want to learn more about difference quotients, you can read:

https://brainly.com/question/4224465

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.