Question

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

Answer 1

D

Explanation:

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

`(f(b)-f(a))/(b-a)`

Here, a is 0 and b is 3, so:
`(f(3)-f(0))/(3-0)=(f(3)-f(0))/(3)`

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

- First term:
`(1)/(2) (3^{3+(1)/(2) })+3=(1)/(2) (3^{3(1)/(2) })+3`

- Second term:
`(1)/(2) (3^{0+(1)/(2) })+3=(1)/(2) (3^{(1)/(2) })+3`

So, the final answer is:

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

Thus, the answer is D.

Hope this helps!