P(xo» Yo) 0 A B (a) The x-intercept of the tangent line is (- F f(x) o). (b) The y-intercept of the tangent line is (0, f(xx) – xof'(x)) (c) The x-intercept of the normal line is (xo + f(xo)f"(xo), O0).

P(xo» Yo) 0 A B (a) The x-intercept of the tangent line is (- F f(x) o). (b) The y-intercept of the tangent line is (0, f(xx) – xof'(x)) (c) The x-intercept of the normal line is (xo + f(xo)f"(xo), O0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 4T

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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:

Question

Let P(x₀, y₀) be an arbitrary point on the graph of f that f′(x0) ≠ 0, as shown in the figure. Verify each statement.

P(xo» Yo)
0 A B
(a) The x-intercept of the tangent line is
(- F
f(x)
o).
(b) The y-intercept of the tangent line is
(0, f(xx) – xof'(x))
(c) The x-intercept of the normal line is
(xo + f(xo)f"(xo), O0).

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