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Lesson 3.1. Slope of a Tangent Line to a Curve Activity 3.1. Find the general equation of the slope of the tangent line to the graph of the following function. Use the concept of the limit of the difference quotient. Show your detailed and complete solution. 1. у %3D х2 — 5х + 8 2. у 3D V5х — 3

Lesson 3.1. Slope of a Tangent Line to a Curve Activity 3.1. Find the general equation of the slope of the tangent line to the graph of the following function. Use the concept of the limit of the difference quotient. Show your detailed and complete solution. 1. у %3D х2 — 5х + 8 2. у 3D V5х — 3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Lesson 3.1. Slope of a Tangent Line to a Curve Activity 3.1. Find the general equation of the slope of the tangent line to the graph of the following function. Use the concept of the limit of the difference quotient. Show your detailed and complete solution. 1. у %3 x2 5x + 8 - 2. у %3D V5x -3 - x2 Activity 3.2. Find the slope of the tangent line to the graph of the function defined by y = 4 + 2x – at (2, 4). Show your detailed and complete solution. Activity 3.3. Find the equation of the tangent line to the curve f at the given value of x. Show your detailed and complete solution. 1. f(x) = 3x² at x = 5 2х-4 2. f(x) at X = -2 %3D Зx+7 Lesson 3.2. Derivative of a Function Activity 3.4. Use the definition of the derivative to find f'(x). Show your detailed and complete solution. 1. f(x) 2. f(x) = 2x + 1 3 3 — 2х —5х2 Activity 3.5. Find the derivative of the given function at a given number. Show your detailed and complete solution. 1. g(x) 3 х2 — 1 at g'(2) - 2х 2. h(x) at h'(-2) x+2
Transcribed Image Text:Lesson 3.1. Slope of a Tangent Line to a Curve Activity 3.1. Find the general equation of the slope of the tangent line to the graph of the following function. Use the concept of the limit of the difference quotient. Show your detailed and complete solution. 1. у %3 x2 5x + 8 - 2. у %3D V5x -3 - x2 Activity 3.2. Find the slope of the tangent line to the graph of the function defined by y = 4 + 2x – at (2, 4). Show your detailed and complete solution. Activity 3.3. Find the equation of the tangent line to the curve f at the given value of x. Show your detailed and complete solution. 1. f(x) = 3x² at x = 5 2х-4 2. f(x) at X = -2 %3D Зx+7 Lesson 3.2. Derivative of a Function Activity 3.4. Use the definition of the derivative to find f'(x). Show your detailed and complete solution. 1. f(x) 2. f(x) = 2x + 1 3 3 — 2х —5х2 Activity 3.5. Find the derivative of the given function at a given number. Show your detailed and complete solution. 1. g(x) 3 х2 — 1 at g'(2) - 2х 2. h(x) at h'(-2) x+2
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