Question

Given f (x) = x2 + 4x + 5, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?

h2 + 8h
2x + h + 4
8 + h
h + 4

Answer 1

By evaluating the quadratic function, we will see that the differential quotient is:

$\frac{f(2 + h) - f(2)}{h} = 8 + h$

How to get (f(2 + h) - f(2))/h?

Here we have the quadratic function:

$f(x) = x^2 + 4x + 5$

Evaluating the quadratic equation we get:

$\frac{f(2 + h) - f(2)}{h}$

So we need to replace the x-variable by "2 + h" and "2" respectively.

Replacing the function in the differential quotient:

$\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}$

If we simplify that last fraction, we get:

$\frac{8h + h^2}{h} = 8 + h$

The third option is the correct one, the differential quotient is equal to 8 + 4.

If you want to learn more about quadratic functions:

https://brainly.com/question/1214333

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