Which function has the greater average rate over the interval [0,3]?f(x) = 2 √(x + 1) - 3x | g(x)---------0 | -21 | -82 | -143 | -20option 1: h(x)option 2: f(x)option 3: g(x)

Question

Which function has the greater average rate over the interval [0,3]?
`f(x) = 2 √(x + 1) - 3`x | g(x)---------0 | -21 | -82 | -143 | -20option 1: h(x)option 2: f(x)option 3: g(x)

Answer 1

For this case we can do the following:

`f(x)=2\sqrt[]{x+1}-3`

We can find:

f(0)= -1 , f(3) = 1

And we have:

`\text{change}=(1+1)/(3-0)=(2)/(3)\text{ }`

For the new function g(x) we have:

`\text{change}=\frac{g(3)-g(0)_{}_{}}{3-0}=(-20+2)/(3-0)=-6`

And for h(x) we have:

`\text{change}=(h(3)-h(0))/(3-0)=(-3-0)/(3-0)=-1`

For this case we can conclude that the greater rate of change needs to be g(x) no matter if is negative since we need to analyze the absolute value