Question

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

Answer 1

Solution

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:

$\text{change}=\frac{1+1}{3-0}=\frac{2}{3}\text{ }$

For the new function g(x) we have:

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

And for h(x) we have:

$\text{change}=\frac{h(3)-h(0)}{3-0}=\frac{-3-0}{3-0}=-1$

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