Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q3

Answer 1

As given by the question

There are given that the function:

`f(x)=x^2+3`

Now,

From the given formula:

`(f(x+h)-f(x))/(h)`

Then,

First find the equation for f(x + h)

So,

`\begin{gathered} f(x)=x^2+3 \\ f(x+h)=(x+h^{})^2+3 \\ f(x+h)=x^2+h^2+2xh+3 \end{gathered}`

Then,

Put both values into the given formula:

So,

`(f(x+h)-f(x))/(h)=(x^2+h^2+2xh+3-x^2-3)/(h)`

Then,

`\begin{gathered} (f(x+h)-f(x))/(h)=(h^2+2xh)/(h) \\ =\frac{h(h^{}+2x)}{h} \\ =h+2x \\ =2x+h \end{gathered}`

Hence, the difference quotient is 2x + h.