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]

left bracket 3 comma 7 right bracket
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Answer 1

Compute the average rate of change for g(x)=√(2x+1) on each interval:

- [0,4]: (g(4)−g(0))/4 = (3−1)/4 = 0.5
- [1,5]: (√11−√3)/4 ≈ 1.5846/4 ≈ 0.3961
- [2,6]: (√13−√5)/4 ≈ 1.3695/4 ≈ 0.3424
- [3,7]: (√15−√7)/4 ≈ 1.2272/4 ≈ 0.3068

The smallest average rate is on [3,7]. So choose [3,7].