a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.

b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

<h3>How to estimate the slope of a tangent line by averaging two adjacent secant lines</h3>

In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:

m = [f(q) - f(p)] / (q - p) (1)

If we know that a = 15 and p = 765, then the slope of the secant lines are:

q = 5, f(q) = 2,076

m = [2,076 - 765] / (5 - 15)

m = - 131.1

q = 10, f(q) = 1,299

m = [1,299 - 765] / (10 - 15)

m = - 106.8

q = 20, f(q) = 357

m = [357 - 765] / (20 - 15)

m = - 81.6

q = 25, f(q) = 84

m = [84 - 765] / (25 - 15)

m = - 68.1

q = 30, f(q) = 0

m = [0 - 765] / (30 - 15)

m = - 51

The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:

m' = [(- 106.8) + (- 81.6)] / 2

m' = - 94.2

The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

To learn more on tangent lines: brainly.com/question/23265136

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2 years ago