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Given f (x) = x2 + 5x + 6, what is [picture included] equal to?


h2 + 14h

2x + h + 5

h + 4

9 + h

Given F X X2 5x 6 What Is Picture Included Equal To H2 14h 2x H 5 H 4 9 H class=

Sagot :

facundo3141592

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

How to find the difference quotient evaluated in 2?

Here we know the function:

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

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

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

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

Learn more about the difference quotient:

https://brainly.com/question/24922801

#SPJ1

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