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:
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