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)
Responses

[1,5]

left bracket 1 comma 5 right bracket

[2,6]

left bracket 2 comma 6 right bracket

[0,4]

left bracket 0 comma 4 right bracket

[3,7]

Answer 1

[3,7]

Reason: g(x)=√(2x+1) has derivative g'(x)=1/√(2x+1), which decreases as x increases. For equal-length intervals, the average rate of change is smaller for larger x, so [3,7] gives the lowest average rate.