Calculus
Calculus
10th Edition
ISBN: 9781285948133
Author: Ron Larson; Bruce H. Edwards
Publisher: Cengage Learning US
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Chapter 1.1, Problem 7E

Secant Lines Consider the function f(x) = 6x– x2 and the point P(2, 8) on the graph of f.

(a) Graph f and the secant lines passing through P(2, 8) and Q(x, f(x)) for x-values of 3, 2.5, and 1.5.

(b) Find the slope of each secant line.

(c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2, 8). Describe how to improve your approximation of the slope.

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Consider the function f(x) = 4x - x² and the point P(1, 3) on the graph of f. (a) Graph fand the secant lines passing through P(1, 3) and Q(x, f(x)) for x-values of 2, 1.5, 0.5. Find the slope of each secant line. line passing through Q(2, f(x)) line passing through Q(1.5, f(x)) line passing through Q(0.5, f(x)) (b) Use the results of part (a) to estimate the slope of the tangent line to the graph of fat P(1, 3). MY NOTES Describe how to improve your approximation of the slope. Define the secant lines with points farther away from P. Choose secant lines that are nearly horizontal. O Define the secant lines with points closer to P. Choose secant lines that are nearly vertical. ASK YOUR TEACHER
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Chapter 1 Solutions

Calculus

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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY