Question

PLEASE SOMEONE HELP ME PLZ

QUICKLY

Answer 1

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

`(f(b)-f(a))/(b-a)`,
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:


`(f(2)-f(1))/(2-1)=6`

For the second function:


`(f(2)-f(1))/(2-1)=f(2)-f(1)=((1)/(4))^2 + 4-[((1)/(4))^1 + 4]= (-3)/(16)`

For the third function, we evaluate based on the graph:


`(f(2)-f(1))/(2-1)=0-(-2)=2`

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.