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Reika [66]
2 years ago
15

Describe how to find the average rate of change between x=3 and x=5 for the function f(x)= 3x^3+2

Mathematics
1 answer:
Anastasy [175]2 years ago
5 0

Answer:

We'll use the traditional "slope" formula, evaluating

\frac{f(5) - f(3)}{5-3}

To find f(5), plug in x = 5 to f(x).

3(5)^3 + 2 = 377

Same thing for f(3)

3(3)^3 + 2 = 83

So

\frac{377-83}{5-3} = \frac{294}{2} = 147

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Answer: The average rate of change is 6.
First, plug in each value of <em>t</em> into the function, v(t) to find there coordinate pairs.

v(2) = (2)^2 - (2) + 10
v(2) = 4 + 8
v(2) = 12

v(5) = (5)^2 - (5) + 10
v(5) = 25 + 5
v(5) = 30

You can write these values as coordinate pairs, like so: (2, 12) and (5, 30).
The formula for the average rate of change is A(x) =  \frac{f(x)-(f(a)}{x-a}. When you plug in the values from this particular case, the average rate of change formula becomes A(t) = \frac{30-12}{5-2}, or A(t)= \frac{18}{3}.

Looking at the equation, you can solve for the average rate of change between t = 2 and t = 5, which equals 6.
8 0
3 years ago
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Roman55 [17]

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Step-by-step explanation:

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Answer:

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