Explanation Given information: y = e x at x = 0 Explanation: The equation of the tangent line to the curve y = f ( x ) at x = a is y − f ( a ) = f ' ( a ) ( x − a ) Here, y = f ( x ) = e x and a = 0 ⇒ f ( 0 ) = e 0 = 1 ⇒ y − 1 = f ' ( 0 ) ( x − 0 ) ⇒ y = f ' ( 0 ) x + 1 Find f ' ( 0 ) using Ti-84 calculator. To find the slope of the graph f ( x ) = e x on Ti-84 calculator using the following steps: Step 1: Select [MATH] [8] and enter the function as d d x ( e x ) | x = 0 Step 2: Hit ENTER to get slope at point x = 0 The calculator gives the value of slope as 1

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 4.2, Problem 53E

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The equation of the tangent to the graph y = ex at x=0. Then, graph the function and the tangent line together to confirm that your answer is correct.

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Chapter 4.2, Problem 52E

Chapter 4.2, Problem 54E

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Calculus & Its Applications (14th Edition)

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The equation of the tangent to the graph y = e x at x = 0 . Then, graph the function and the tangent line together to confirm that your answer is correct.

Solution Summary: The author explains how to determine the equation of the tangent to the graph yex. They then graph the function and the line together to confirm that their answer is correct.

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The equation of the tangent to the graph y = ex at x=0. Then, graph the function and the tangent line together to confirm that your answer is correct.

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Chapter 4 Solutions