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d) What is the derivative of f(x) at a = -4? e) Now, recall that, in the first part of the semester, we viewed f'(-4) as the instan- taneous rate of change at -4, and we guessed the numerical value of the instantaneous rate of change by looking at average rates of change over smaller and smaller intervals. For example, in order to find f'(-4), we had to calculate the average rates of change of y = f(x) = -z² - 4x -3 over intervals such as: i) [-4,–3.9) ii) [-4,-3.99]

d) What is the derivative of f(x) at a = -4? e) Now, recall that, in the first part of the semester, we viewed f'(-4) as the instan- taneous rate of change at -4, and we guessed the numerical value of the instantaneous rate of change by looking at average rates of change over smaller and smaller intervals. For example, in order to find f'(-4), we had to calculate the average rates of change of y = f(x) = -z² - 4x -3 over intervals such as: i) [-4,–3.9) ii) [-4,-3.99]

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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Use this function to solve for Question 1E
Problem Set B.pdf 1. Consider the function f(x) = -x² – 4x – 3
Transcribed Image Text:Problem Set B.pdf 1. Consider the function f(x) = -x² – 4x – 3
d) What is the derivative of f(æ) at a = -4? e) Now, recall that, in the first part of the semester, we viewed f'(-4) as the instan- taneous rate of change at -4, and we guessed the umerical value of the instantaneous rate of change by looking at average rates of change over smaller and smaller intervals. For example, in order to find f'(-4), we had to calculate the average rates of change of y = f(x) = -x² – 4x – 3 over intervals such as: i) [-4, –3.9] ii) [–4, –3.99] 3 iii) [–4,–3.999)], as well as over intervals such as: i) [-4.1, --4] ii) [-4.01, –4] iii) [-4.001, –4] Based on the numerical values of the above average rates of change, what is the instan- taneous rate of change at z = -4 be? Does this answer agree with the answer from part d)? Explain. Draw a large and clear sketch of the graph of f(x), as well as the tangent line at point P(-4, -3). As discussed in class, from a geometric point of view, f'(-4) represents the slope of the tangent line to the given curve at point P. You may also want to check your work on the graphing calculator.
Transcribed Image Text:d) What is the derivative of f(æ) at a = -4? e) Now, recall that, in the first part of the semester, we viewed f'(-4) as the instan- taneous rate of change at -4, and we guessed the umerical value of the instantaneous rate of change by looking at average rates of change over smaller and smaller intervals. For example, in order to find f'(-4), we had to calculate the average rates of change of y = f(x) = -x² – 4x – 3 over intervals such as: i) [-4, –3.9] ii) [–4, –3.99] 3 iii) [–4,–3.999)], as well as over intervals such as: i) [-4.1, --4] ii) [-4.01, –4] iii) [-4.001, –4] Based on the numerical values of the above average rates of change, what is the instan- taneous rate of change at z = -4 be? Does this answer agree with the answer from part d)? Explain. Draw a large and clear sketch of the graph of f(x), as well as the tangent line at point P(-4, -3). As discussed in class, from a geometric point of view, f'(-4) represents the slope of the tangent line to the given curve at point P. You may also want to check your work on the graphing calculator.
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