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1. Let f(x) = x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0, 1) by directly evaluating the limit: f'(0) = lim Δx-0 f(Ax)-f(0) Ax - ƒ(0)) (b) Find the equation of the tangent line What are the x and y intercepts of 1? to the graph off at P. (c) Find the equation of the line, n, through P that is perpendicular to the tangent line (Line n is called the normal line to the graph of f at P.) (d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its tangent and normal lines at point P, and the x and y intercepts of these lines.

1. Let f(x) = x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0, 1) by directly evaluating the limit: f'(0) = lim Δx-0 f(Ax)-f(0) Ax - ƒ(0)) (b) Find the equation of the tangent line What are the x and y intercepts of 1? to the graph off at P. (c) Find the equation of the line, n, through P that is perpendicular to the tangent line (Line n is called the normal line to the graph of f at P.) (d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its tangent and normal lines at point P, and the x and y intercepts of these lines.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let f(x)=x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly evaluating the limit: f'(0) = lim Ax-0 ( f (Ax) = f(0)). - Ax (b) Find the equation of the tangent line to the graph off at P. What are the x and y intercepts of 1? (c) Find the equation of the line, n, through P that is perpendicular to the tangent line (Line n is called the normal line to the graph of f at P.) (d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its tangent and normal lines at point P, and the x and y intercepts of these lines. Bonus: Find the coordinates of the second point, Q, (Q P), at which the normal line n intersects the graph of f.
Transcribed Image Text:1. Let f(x)=x² - 2x + 1. (a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly evaluating the limit: f'(0) = lim Ax-0 ( f (Ax) = f(0)). - Ax (b) Find the equation of the tangent line to the graph off at P. What are the x and y intercepts of 1? (c) Find the equation of the line, n, through P that is perpendicular to the tangent line (Line n is called the normal line to the graph of f at P.) (d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its tangent and normal lines at point P, and the x and y intercepts of these lines. Bonus: Find the coordinates of the second point, Q, (Q P), at which the normal line n intersects the graph of f.
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