Question

Compare the estimated average rates of change of the functions f(x)=3.5x2
and g(x)=3.5x
over the interval [1,2.39]
.(1 point)

The estimated average rates of change of both functions over the interval [1,2.39]
are approximately equal.

The estimated rate of change of f(x)
is greater than the estimated rate of change of g(x)
over the interval [1,2.39]
.

Answer 1

Compute the average rates:

- For g(x)=3.5x (linear), the average rate over any interval is the slope 3.5.
- For f(x)=3.5x^2, average rate over [1,2.39] = [f(2.39)-f(1)]/(2.39-1)
= 3.5(2.39^2−1^2)/(2.39−1) = 3.5(2.39+1) = 3.5·3.39 ≈ 11.865.

So the estimated rate of change of f(x) (≈11.865) is greater than that of g(x) (3.5).