The remaining problems will refer to the following table, which shows the average price of one...

The remaining problems will refer to the following table, which shows the average price of one gallon of gas in the United States over the past few weeks. (Data from ycharts.com/indicators/us gas price)

Date March 2 March 9 March 16 March 23 March 30

Price per gallon $2.514
$2.468
$2.343

$2.217 $2.103

Let f(t) be the price of one gallon of gas t days after February 29. (So, for example, the table shows that f(9) = 2.468.) Estimate f′(30).
Use your estimate to find the linearization of f(t) at t = 30.
Use your linearization to approximate the price for one gallon of gas on April 10.
Would it be reasonable to use your linearization to approximate the price of one gallon of gas on October 31? Why or why not?

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Expert Solution

milcah answered 1 year ago

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