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Nata [24]
2 years ago
5

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?

Mathematics
1 answer:
meriva2 years ago
8 0

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

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

<h3>How to get (f(2 + h) - f(2))/h?</h3>

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:

brainly.com/question/1214333

#SPJ1

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