Question

I need help with this question

Answer 1

7

Explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function:
`f(x)=x^2+3x`

Intervale,
`[0, 4]`

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane (
`x, y`). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

`(y_2-y_1)/(x_2-x_1)`

Where (
`x_1,y_1`) and (
`x_2,y_2`) are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

`f(x)=x^2+3x`

[ 0, 4 ]

`f(0)=(0)^2+3(0)\\=0 + 0\\ =0`

Point: (0, 0)

`f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28`

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

`(y_2-y_1)/(x_2-x_1)`

(0, 0), (4, 28)

Substitute,

`(y_2-y_1)/(x_2-x_1)\\\\=(28-0)/(4-0)\\\\=(28)/(4)\\\\= 7`

The average rate of change is 7.

Answer 2

7

This question is tying to introduce an idea that

eventually becomes a calculus question ....

(4^2 + 3(4)) - (0^2+3(0))

4 - 0

28 - 0 = 7

4

Explanation: