Question

I need help with this question

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

7

Step-by-step 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,

$\frac{y_2-y_1}{x_2-x_1}$

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

$\frac{y_2-y_1}{x_2-x_1}$

(0, 0), (4, 28)

Substitute,

$\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7$

The average rate of change is 7.