Question

Please answer this question

Answer 1

Answer:

The answer is

Step-by-step explanation:

Given: f(x) = 3 + 2x - x²

To compute f(3 + h) substitute x = 3 + h.

Similarly, to compute f(h) simply substitute x = h.

We are asked to compute $\frac{f(3 + h) - f(h)}{h}$

f(3 + h) = 3 + 2(3 + h) - {(3 + h)²}

           = 3 + 6 + 2h - {9 + 6h + h²}

           = 9 + 2h - 9 - 6h - h²

           = - 4h - h²

Now, f(h) = 3 + 2h - h²

f(3 + h) - f(h) = -4h - h² - 3 - 2h + h²

                    = -6h - 3

$\therefore \frac{f(3 + h) - f(h)}{h} = \frac{-3(2h + 1)}{h}$ which is the required answer.