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3 years ago

Let f(x)=x2+6x+11. What is the average rate of change from x = 5 to x = 8?

Mathematics

2 answers:

svlad2 [7]3 years ago

7 0

Answer: the answer is 19

Step-by-step explanation:

Korvikt [17]3 years ago

6 0

Plug 8 into the equation and divide it by that equation but with 5 plugged in

$\frac{ {8}^{2} + 6(8) + 11}{ {5}^{2} + 6(5) + 11 }$

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Svet_ta [14]

Answer:

$A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36$

Step-by-step explanation:

The equations are:

$y = x^{2} + 2x + 3$

$y = 2x + 12$

The two graphs intersect when:

$x^{2} + 2x + 3 = 2x + 12$

$x^{2} = 0$

$x_{1} = 3\\x_{2} = -3$

To find the area under the curve for the first equation:

$A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

To find the area under the curve for the second equation:

$A_{2} = \int\limits^3__-3}{2x + 12} \, dx$

To find the total area:

$A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

Simplifying the equation:

$A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx$

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).

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3 years ago

Let ​ f(x)=x2+6x+11​. What is the average rate of change from x = 5 to x = 8?

Let f(x)=x2+6x+11. What is the average rate of change from x = 5 to x = 8?