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Readme [11.4K]
3 years ago
7

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:

\frac{\Delta y}{\Delta x}  =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1}  =\frac{f(x_2)-f(x_1)}{x_2-x_1}

So, the average rate of change of:

f(x)=-x^2+3x+6

Over the interval -3

Is:

f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12

\frac{\Delta y}{\Delta x}  =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3

Therefore, the average rate of change of this function over that interval is 3.

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F(x) = 11x³ - 6x² + x + 3
anzhelika [568]

Answer:

3

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the value of y in the equation 5x + 2y = 20, when x = 0.3?
Dimas [21]
Y=9.25 (short answer but hope this helped u)
5 0
3 years ago
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Thanks for your response!<br> Question will be show✔
algol13
<h3>Answer:</h3>

\large\boxed{-1\frac{16}{25},\,\frac{6}{40},\,0.35,\,1\frac{3}{4}}

<h3>Step-by-step explanation:</h3>

In this question, it's asking you to put the numbers that were given from <em>least </em>to <em>greatest.</em>

Our given numbers are:

  • \frac{6}{40}
  • 0.35
  • 1\frac{3}{4}
  • -1\frac{16}{25}

Now, lets sort them out.

We know that negative numbers would be the least. Sicne there's only one negative number, we would put that first because it's the least out of the numbers.

\frac{6}{40} would go next. To make it easier, we can turn it into a decimal. \frac{6}{40} = 0.15 when you divide.

0.35 will go next. This would be bigger than 0.15, but lower than the next number.

1\frac{3}{4} would go last, due to the fact that it's the greatest. 1\frac{3}{4} is the same as 1.75

When you put them in order, you should get -1\frac{16}{25},\,\frac{6}{40},\,0.35,\,1\frac{3}{4}

<h3>I hope this helped you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>
4 0
3 years ago
If -1 &lt; x &lt; 0 which of the following has the smallest value?
Katyanochek1 [597]

Answer: (B) x^3

Explanation:

If you compare the graphs of

  • y = x^2
  • y = x^3
  • y = x^4

all on the interval -1 < x < 0, you'll find that y = x^3 is the smallest when x = -1

Squaring a negative number leads to a positive result, and similarly that happens with x^4 as well. This is because x^4 = (x^2)^2.

Plugging x = -1 into x^3 leads to y = -1 as a result.

6 0
2 years ago
Simplify 7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54
Katen [24]
7\sqrt3-4\sqrt6+\sqrt{48}-\sqrt{54}\\\\=7\sqrt3-4\sqrt6+\sqrt{16\cdot3}-\sqrt{9\cdot6}\\\\=7\sqrt3-4\sqrt6+\sqrt{16}\cdot\sqrt3-\sqrt9\cdot\sqrt6\\\\=7\sqrt3-4\sqrt6+4\sqrt3-3\sqrt6\\\\=\boxed{11\sqrt3-7\sqrt6}
3 0
2 years ago
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