Answer:
Step-by-step explanation:
One formula for "average rate of change" is
f(b) - f(a)
a. r. c. = ------------------- = (increase in y) / (increase in x
b - a
In the case of this particular function, a = 0, b = 4, and the related y-values are f(a) = f(0) = -3, f(b) = f(4) = 0, and so the average rate of change of this function on (0, 4) is
f(4) - f(0) 0 - (-3)
a. r. c. = ---------------- = --------------- = +3/4
4 - 0 4
Therefore, "The average rate of change between [0,4] is positive" is true.
f(4) - f(-3) 0 - (0)
a. r. c. = ---------------- = --------------- = 0 (not 7)
4 - 0 4
Therefore, "The average rate of change between [-3,4] is positive" is false. The average r. of c. is actually 0. (Again, see above).
From above,
f(4) - f(0) 0 - (-3)
a. r. c. = ---------------- = --------------- = +3/4 This is true
4 - 0 4
