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Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the graph of f(x) at any point. (b) Find the slope of the tangent at the given point. (c) Write the equation of the line tangent to the graph of f(x) at the given point. (Let x be the independent variable and y be the dependent variable.) (d) Graph both f(x) and its tangent line (use a graphing utility).

Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the graph of f(x) at any point. (b) Find the slope of the tangent at the given point. (c) Write the equation of the line tangent to the graph of f(x) at the given point. (Let x be the independent variable and y be the dependent variable.) (d) Graph both f(x) and its tangent line (use a graphing utility).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 41E
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Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the graph of f(x) at any point. (b) Find the slope of the tangent at the given point. (c) Write the equation of the line tangent to the graph of f(x) at the given point. (Let x be the independent variable and y be the dependent variable.) (d) Graph both f(x) and its tangent line (use a graphing utility). -4 O -4 y 4 3 3 2 1 2 2 4 X X i -6 -4 -2 y 2 4 X -4 y 4 3 2 1 2 X +
Transcribed Image Text:Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the graph of f(x) at any point. (b) Find the slope of the tangent at the given point. (c) Write the equation of the line tangent to the graph of f(x) at the given point. (Let x be the independent variable and y be the dependent variable.) (d) Graph both f(x) and its tangent line (use a graphing utility). -4 O -4 y 4 3 3 2 1 2 2 4 X X i -6 -4 -2 y 2 4 X -4 y 4 3 2 1 2 X +
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