Question

What is the average Rate of Change for the function f(x) = x ^ 2 + 7x - 4 over the interval [0, 2]

Answer 1

Answer:

The average rate of change of function f over the interval [0, 2] is 9.

Step-by-step explanation:

To find the average rate of change of a function over an interval, we evaluate the function at the endpoints of the interval and find the slope between them.

We are given the function:

$f(x)=x^2+7x-4$

And we want to find its average rate of change over the interval [0, 2].

So, evaluate the function at the endpoints:

$f(0)=(0)^2+7(0)-4=-4$

$f(2)=(2)^2+7(2)-4=14$

And find the slope between them:

$\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{14-(-4)}{2-0}=\frac{18}{2}=9$

So, the average rate of change of function f over the interval [0, 2] is 9.