Question

Determine which function has the greatest rate of change as x approaches infinity.A). f(x) = 2x − 8B). g(x) = 5x^2 − x + 7C). h(x) = 4^x − 6D). There is not enough information to determine the answer.

Answer 1

We need to find the derivative which is the rate of change

`\begin{gathered} f^(\prime)(x)=2 \\ g^(\prime)(x)=10x\text{ - }1\text{ + 7} \\ g^(\prime)(x)=10x+6 \\ h^(\prime)(x)=4 \end{gathered}`

So, when x is infinite, the function g(x) has the greatest rate of change