What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 2]?
x | f(x)
-5 -150
-3 -36
-1 -2
0 0
1 0
2 4

a) -40
b) -8
c) 8
d)32

Option c) 8 is the answer.

Step-by-step explanation:

Given table is

x         -5      -3       -1       0        1        2

f(x)    -150   -36      -2      0        0       4

We have to find the rate of change of f(x) over the period of x  [-3, 2]

Since rate of change of x =

Now we have been given

and

Similarly

Now rate of change of f(x) will be =

Option C is the answer.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

i think its a and d

step-by-step explanation: