We want to get the difference quotient for the given function, we will get see that the difference quotient is equal to:
f'(x) = 2x + 5
<h3>The difference quotient:</h3>
For a given function f(x), we define the difference quotient as:
In this case, we have:
f(x) = x^2 + 5x + 6
Replacing that in the difference quotient we get:
Now we can cancel the factor h to get:
So the difference quotient is equal to 2x + 5.
If you want to learn more about difference quotients, you can read:
Answer:
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
In which m is the slope, and b is the y-intercept(value of y when x = 0).
In this question:
We have that when . So the line is given by:
Finding the slope:
We have two points in the line, which are (-3,-3) and (3,-1). The slope is given by the change in y divided by the change in x. So
Change in y: -1 - (-3) = -1 + 3 = 2
Change in x: 3 - (-3) = 3 + 3 = 6
Slope:
Solution to the inequality:
The solution to this inequality is all the points above the dashed line, which means that the dashed line is not part of the solution. So