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3 years ago

What is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Mathematics

1 answer:

Neko [114]3 years ago

5 0

Answer:

Step-by-step explanation:

For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.

The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...

f'(1) = 2(1) = 2

The average rate of change of f(x) on [-2, 4] is 2.

Alternate solution

The average rate of change is the slope of the line between the end points of the interval:

m = (y2 -y1)/(x2 -x1)

m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2

The average rate of change on [-2, 4] is 2.

_____

The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.

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Choose the Algebraic equation that matches the table

juin [17]

Answer:

Step-by-step explanation:

In order to write the equation, you need to identify the slope and y-intercept.

1) the y intercept is what y is when x=0. According to the table, it is -2.

2) the slope is the change in the y values over the change in the x values. Notice that the y values are increasing by one for every increase in 1 in the x values, so the slope is 1/1 or 1.

3) we can then put those values into slope-intercept form which is y=mx+b where m is the slope and b is the intercept.

4) so the equation is y=(1)x-2 or y=x-2 (they are the same)

8 0

3 years ago

Need help with finding the area of this

dusya [7]

In the given figure, there are two right angled triangles.

Area of triangle = 1/2 × b × h

Area of shaded region = area of larger triangle - area of smaller triangle

= 1/2 × 15 × 18 - 1/2 × 8 × 9

= 135 - 36

= 99 ft^2

Thus, area of shaded region is 99 ft^2.

3 0

3 years ago

How can I create a word problem with the following expressions 15+2d 200-4m

Alenkasestr [34]

For the first expression
15 + 2d
A possible word problem would be this:
A person saves $2 per day of money. Before he started saving, he had $15 dollars set aside. Look for the expression that expresses the total amount of money saved in terms of the number of days passed

The second expression is
200 - 2m
A possible word problem would be this:
The distance from school to the park is 200m. A kid riding a bike is traveling at a speed of 2m/s from the school to the park. Write an expression for the distance remaining between the park and the kid.

6 0

2 years ago

Moselle is riding a roller coaster that is 155 feet high.

DerKrebs [107]

Answer:

Step-by-step explanation:

155-16s²

155- 16x2²

155- 16x4

155-64

5 0

2 years ago

15 points!

Phantasy [73]

Hi there! You are provided with two points, this is all you need to calculate the line's slope.

The equation for slope is:

$\frac{y2 - y1}{x2 - x1}$

$\frac{10 - 8}{3 - 7} = -\frac{2}{4}$

Slope: -2/4

Point slope form, or y-y1 = m(x - x1). All we have to do is take the x and y coordinates of either point, as well as the slope, and plug them into the equation.

y - 10 = -2/4(x - 3)

Write the equation in slope-intercept form (y=mx+b)

$y - 10 = -2/4(x-3)\\y = -2/4(x-3) + 10\\y = -2/4x + 1.5 + 10\\y = -2/4x + 11.5$

A) -2/4

B) y - 10 = -2/4(x - 3)

C) y = -2/4x + 11.5

8 0

2 years ago