Question

F(x)=x^2+10 Over which interval does fff have a positive average rate of change?

Answer 1

Answer:

(0, inf)

Step-by-step explanation:

The average rate of change of a function is related to it's first derivative. When the first derivative is positive, the average rate of change is positive, which means that the function is crescent.

Now, when the first derivative is negative, the average rate of change will be negative too, and the function is going to be decrescent.

In your function.

We have: f'(x) = 2x

2x > 0 when x > 0. So when x > 0 the average rate of change of your function is positive, and it's values increases as the time increases. When x < 0, the average rate of change is negative, so, as the time increases, the values of f decrease.

You can use a graphic tool to plot f and visualize this better.

Answer 2

Answer:

The answer is  [-1,2]

Hope it helps