Explanation Given: The function, y = 3 x 2 − x 3 and the point ( 1 , 2 ) Concept Used: Slope of the tangent line of a function f ( x ) at any point x = c is given by the first derivative at that point. That is the slope of tangent line at x = c is given by f ′ ( c ) . Slope of the normal line at any point of the curve is equal to the negative reciprocal of the slope of tangent line. That is the slope of tangent line at x = c is given by − 1 f ′ ( c ) . The point-slope form of the line passing through the point ( x 1 , y 1 ) and having slope m is given by y − y 1 = m ( x − x 1 ) . Power rule of derivatives, d d x ( x n ) = n x n − 1 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: Consider the function, y = 3 x 2 − x 3 In order to find the equation of tangent line, first find the slope of tangent line by finding the first derivative at the specified point

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.3, Problem 40E

To determine

The equation of the tangent lineto the curve y=3x2−x3 at the point (1,2) , and plot the graph of curve and tangent line on same screen.

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Chapter 3.3, Problem 39E

Chapter 3.3, Problem 41E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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Implicit Differentiation Explained - Product Rule, Quotient & Chain Rule - Calculus; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=LGY-DjFsALc;License: Standard YouTube License, CC-BY

The equation of the tangent lineto the curve y = 3 x 2 − x 3 at the point ( 1 , 2 ) , and plot the graph of curve and tangent line on same screen.

Solution Summary: The author plots the graph of the curve and tangent line on the same screen using the power rule of derivatives.

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The equation of the tangent lineto the curve y=3x2−x3 at the point (1,2) , and plot the graph of curve and tangent line on same screen.

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Chapter 3 Solutions