All categories

3 years ago

Arrange these functions from the greatest to least value based on the average rate of change in the specified interval.

1 answer:

3 0

Let us create a table that evaluates the slope of each function within its specified interval.

Define
[x1,x2] = the specified interval
f1 = f(x1)
f2 = f(x2)

The average rate of change is the slope, calculated as
Slope = (f2 - f1)/(x2 - x1)

f(x) Interval x2-x1 f1 f2 Slope
----------- ----------- -------- -------- ---------- ---------
x² + 3x [-2, 3] 5 -2 18 4
3x - 8 [4, 5] 1 4 7 3
x² - 2x [-3, 4] 7 15 8 -1
x² - 5 [-1, 1] 2 -4 -4 0

Answer:
In order of the greatest slope to the lowest slope, the order of the functions is 1, 2, 4 and 3. That is,
1. f(x) = x² + 3x
2. f(x) = 3x - 8
4. f(x) = x² - 5
3. f(x) = x² - 2x

You might be interested in

A quadratic equation is shown below:

sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

$3x^{2}-11x+10=0$ has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

$\frac{d}{dx}(3x^{2}-11x+10)=6x-11$

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

$x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}$

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

$x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}$

6 0

3 years ago

Apples sell for $1.90 per pound, and bananas sell for $0.75 per pound. Troy bought some apples and some bananas. Together they w

matrenka [14]

Answer:

1.15p + 285 = 5.84

Step-by-step explanation:

This problem has two equations. Total cost and Total pounds. The cost and the pounds

p = apple pounds

b = banana pounds

Cost

1.90p + .75b = 5.84

Pounds

p + b = 3.8

Now we use the substitute method for system of equations to solve

p + b = 3.8

b = -p + 3.8

Now that we know what b equals, substitute is for b in the cost equation.

1.90p + .75b = 5.84

1.90p + .75(-p+3.8) = 5.84

distribute / multiply .75 by (-p+3.8)

1.90p + -.75p + 2.85 = 5.84

Combine the p values

1.15p + 285 = 5.84

4 0

3 years ago

help me brainlist if you right Mona is inviting 10 friends to a party. Each friend wants 5 cookies and each box has 10 cookies.

seropon [69]

Answer:

its 5 boxes

Step-by-step explanation:

5 0

2 years ago

Is 42(x + 14y) equivalent to 42x - 56y

g100num [7]

Answer:

No its not

Step-by-step explanation:

When 42(x + 14y) is simplified:

42(x + 14y)

Expand and remove the brackets. Remember brackets mean to multiply.

42*x

42x

42*14y

588y

42x+588y

Therefore 42x-56 is NOT EQUIVALENT to 42(x + 14y) but is equivalent to 42+588y

3 0

3 years ago

(4,-2) and (-2,-2) write the equation.

bixtya [17]

the equation is Y=-2/3x+2/3

8 0

3 years ago