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Maksim231197 [3]
1 year ago
15

Which function has an average rate of change of -4 over the interval [-2,2]?

Mathematics
1 answer:
kolbaska11 [484]1 year ago
8 0

Only p(x) has an average rate of change of -4 over [-2, 2].

Find the average rate of change of each given function over the interval [-2, 2]]:

The average rate of change of m(x) over [-2, 2]:

<h3>What is the average rate?</h3>

The average rate of change = \frac{m(b)-m(a)}{b-a}

Where, a = -2, m(a) = -12

b = 2, m(b) = 4

Plug the values into the equation

The average rate of change

=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}

The average rate of change = 4

The average rate of change of n(x) over [-2, 2]:

The average rate of change = \frac{n(b)-n(a)}{b-a}

Where, a = -2, n(a) = -6

b = 2, n(b) = 6

Plug the values into the equation

The average rate of change

=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}

The average rate of change = 3

The average rate of change of q(x) over [-2, 2]:

The average rate of change = \frac{q(b)-q(a)}{b-a}

Where, a = -2, q(a) = -4

b = 2, q(b) = -12

Plug the values into the

The average rate of change = \frac{-4-12}{2-(-2)}

= \frac{-16}{4}

The average rate of change = -2

The average rate of change of p(x) over [-2, 2]:

The average rate of change = \frac{p(b)-p(a)}{b-a}

Where, a = -2, p(a) = 12

b = 2, p(b) = -4

Plug the values into the equation

The average rate of change = \frac{-4-12}{2-(-2)}

=\frac{-16}{4}

The average rate of change = -4

The answer is D.

Only p(x) has an average rate of change of -4 over [-2, 2].

To learn more about the average rate of visit:

brainly.com/question/8728504

#SPJ1

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Answer:

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Step-by-step explanation:

Hi there!

Slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x=0)

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

m=\displaystyle \frac{y_2-y_1}{x_2-x_1} where two points that fall on the line are (x_1,y_1) and (x_2,y_2)

Given the graph, we determine which points we could use. For example, we could use the two points (0,2) and (1,-4):

m=\displaystyle \frac{-4-2}{1-0}\\\\m=\displaystyle \frac{-6}{1}\\\\m=-6

Therefore, the slope of the line is -6. Plug this into y=mx+b:

y=-6x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

Recall that the y-intercept occurs when x=0. Given the point (0,2), we know that the y-intercept is 2. Plug this into y=-6x+b:

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Mrs. Del Pup bought 20 yards of border for her classroom bulletin board.
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So, all the possible areas are given by the product of the dimensions, i.e.

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The function f(x)=-x^2+10x represents a parabola, facing downwards, and thus it admits a maximum, which is its vertex.

In particular, the vertex of this parabola is given by

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(b)The dimensions of the rectangle with greatest area are x=5 and y=10-x=10-5=5, so it's actually a square.

This is a well known theorem: if you fix the perimeter, the rectangle with the largest area is the square yielding that perimeter.

(c) If we increase both dimensions by 2 yards, our 5x5 square would become a 7x7 square...

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