Q(x)=x^2-5x+1, find Q(2+h)-Q(2)/h. I don't know how to input this.

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The given function is `Q ( x ) = x^2 - 5 x + 1 ,` the expression to evaluate is

`( Q ( 2 + h ) - Q ( 2 ) ) / h .`

It shows how quickly `Q ( x )` increases near `x = 2 .` This expression is also the starting one to find the derivative of `Q ( x )` at `x = 2` which also tells us about the grows of `Q` near `x = 2 .`

Let's start from `Q ( 2 + h ) ,` which means to substitute `x + 2` instead of `x` to the expression of `Q ( x ) :`

`Q ( 2 + h ) = ( 2 + h )^2 - 5 ( 2 + h ) + 1 = 2^2 + 2*2*h + h^2 - 10 - 5 h + 1.`

Then subtract `Q ( 2 ) ,` some summands disappear:

`2^2 + 2*2*h + h^2 - 5*2 - 5 h + 1 - 2^2 + 5*2 - 1 =`

`= 4h + h^2 - 5h = h^2 - h .`

Now we can divide this by `h` and it actually divides:

`( h^2 - h ) / h ` = h - 1.

It is the answer. When we'd find the derivative, h will tend to zero and the limit will be obviously `- 1 ,` which is correct.

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