Question

Which expression both gives the average rate of change of the function h(x)

Answer 1

Answer:

D

Step-by-step explanation:

The average rate of change of a function over an interval a ≤ x ≤ b is found by:

$\frac{f(b)-f(a)}{b-a}$

Here, a is 0 and b is 3, so: $\frac{f(3)-f(0)}{3-0}=\frac{f(3)-f(0)}{3}$

Just plug in 3 for the first term and 0 for the second term in the numerator:

- First term: $\frac{1}{2} (3^{3+\frac{1}{2} })+3=\frac{1}{2} (3^{3\frac{1}{2} })+3$

- Second term: $\frac{1}{2} (3^{0+\frac{1}{2} })+3=\frac{1}{2} (3^{\frac{1}{2} })+3$

So, the final answer is:

$\frac{[\frac{1}{2} (3^{3\frac{1}{2} })+3]-[\frac{1}{2} (3^{\frac{1}{2} })+3]}{3}$

Thus, the answer is D.

Hope this helps!