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aniked [119]
3 years ago
11

Given the function, f(x) = x2 - 3, calculate the average rate of change of the function from x = 1 to x = 3.

Mathematics
2 answers:
Crank3 years ago
7 0

\bf slope = m = \cfrac{rise}{run} \implies  \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby  \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= x^2-3  \qquad  \begin{cases} x_1=1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(1)}{3-1} \\\\\\ \cfrac{[3^2-3]-[1^2-3]}{2}\implies \cfrac{6 - (-2)}{2}\implies \cfrac{6+2}{2}\implies \cfrac{8}{2}\implies 4

Valentin [98]3 years ago
3 0

Answer: 4

Step-by-step explanation:

The given function : f(x) = x^2 - 3

The average rate of change in a function g(x) from x=a to x=b is given by :-

k=\dfrac{g(b)-g(a)}{b-a}

Then, the average rate of change of the given function from x = 1 to x = 3 will be :-

k=\dfrac{f(3)-f(1)}{3-1}\\\\=\dfrac{(3)^2-3-(1^2-3)}{2}=\dfrac{9-3-1+3}{2}\\\\=\dfrac{8}{2}=4

Hence, the average rate of change of the function from x = 1 to x = 3 is 4.

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<em><u>Question:</u></em>
<em>Mrs. Magdalino kept records on how much she spent on gasoline and the maintenance of her car.  She found that it cost $485 to drive 500 mi in a month.</em>
<em>a)  Find the cost per mile.  Write an equation that relates the cost c for gasoline and maintenance of a car to the number of miles m the car is driven.</em>
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<em><u>Answer:</u></em>
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$485/500mi = <u><em>$0.97/mi</em></u>

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(1200 mi)*($0.97/mi) = <u><em>$1164</em></u>

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