Question

Consider the cubic function d(x)=2x−1−−−−−√3
and the square root function g(x)=2x+1−−−−−√
. Select the interval where the square root function has the lower estimated average rate of change.(1 point)

[0,4]


[1,5]


[2,6]


[3,7]

Answer 1

[0,4]

Reason: g(x)=√(2x+1) has average rate (g(4)-g(0))/4 = (3−1)/4 = 0.5, while d(x)=∛(2x−1) has (∛7−∛(−1))/4 ≈ (1.913−(−1))/4 ≈ 0.728. On the other intervals g's average rate is larger than d's.