Need with algebra these functions from the greatest to the least value based on the average rate of change in the specified interval. need the answers asap

We know that the average rate of function f(x) from x=a to x=b i.e. in the interval [a,b] is calculated as follows:

a)

interval: [-2,3]

We have:

and

The average rate of change is calculated as:

Hence, Average rate of change is: 4

b)

interval: [4,5]

and

The average rate of change is calculated as:

Hence, Average rate of change is: 3

c)

interval : [-3,4]

The average rate of change is calculated as:

Hence, Average rate of change is: -1

d)

interval : [-1,1]

and

The average rate of change is calculated as:

Hence, Average rate of change is: 0

Hence, on arranging the functions from greatest to least value based on average rate of change in the specified interval is:

i.e.   a < b < d < c

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.