Question

Compare the estimated average rates of change of the functions f(x)=3x−4−−−−−√
and g(x)=2x−43−−−−−√3
over the interval [2,3]
. State the difference in the estimated average rates of change to the nearest tenth.(1 point)
The difference between the estimated average rates of change is approximately
.

Answer 1

f(3)-f(2) = √(9−4) − √(6−4) = √5 − √2 ≈ 2.2361 − 1.4142 = 0.8219
g(3)-g(2) = ∛(6−4) − ∛(4−4) = ∛2 − 0 ≈ 1.2599

Difference ≈ 1.2599 − 0.8219 = 0.4380 ≈ 0.4

The difference between the estimated average rates of change is approximately 0.4.