Simplify this expressions
1 answer:
You might be interested in
You've probably seen the average rate of change before, when it's called the slope of a line. The difference here is that you are looking at a curve, not a straight line. We can talk about the slope of a line through two points on the curve, that is, through x = 1 and x = 2 given by the interval [1,2]. FYI, this is called the secant line. Now, this is probably more detail than you wanted...
We have a bunch of different ways to calculate the average rate of change.
The most straightforward for a function f(x) is to write
,
and b can't equal a if we're not dealing with calculus.
So for the first function, we take our two points, 1 and 2, and look at the function definition and evaluate:
For the second function:
![\dfrac{f(2)-f(1)}{2-1}=f(2)-f(1)=(\dfrac{1}{4})^2 + 4-[(\dfrac{1}{4})^1 + 4]= \dfrac{-3}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7Bf%282%29-f%281%29%7D%7B2-1%7D%3Df%282%29-f%281%29%3D%28%5Cdfrac%7B1%7D%7B4%7D%29%5E2%20%2B%204-%5B%28%5Cdfrac%7B1%7D%7B4%7D%29%5E1%20%2B%204%5D%3D%20%5Cdfrac%7B-3%7D%7B16%7D%20)
For the third function, we evaluate based on the graph:
Now, we move onto the question. None of these have the same average rates of change, so we eliminate A and D. Comparing the average rates of change, it is true that function 2 has the lowest, so we choose B.
We have a bunch of different ways to calculate the average rate of change.
The most straightforward for a function f(x) is to write
and b can't equal a if we're not dealing with calculus.
So for the first function, we take our two points, 1 and 2, and look at the function definition and evaluate:
For the second function:
For the third function, we evaluate based on the graph:
Now, we move onto the question. None of these have the same average rates of change, so we eliminate A and D. Comparing the average rates of change, it is true that function 2 has the lowest, so we choose B.