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Consider the following function: f(x) = 3x – 2x? a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2)

Consider the following function: f(x) = 3x – 2x? a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2)

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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1. Consider the following function: f (x) = 3x – 2x2 a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2) Given the graph of a function f(x), which is shown to the right, sketch the graph of its derivative f'(x), on the same xy-plane. *Assume the scales of the x-axis and the y-axis are equal.* 2.
Transcribed Image Text:1. Consider the following function: f (x) = 3x – 2x2 a. Find the derivative function f'(x) using the limit definition of the derivative. b. Use the derivative function to evaluate f'(-1) and f'(2) Given the graph of a function f(x), which is shown to the right, sketch the graph of its derivative f'(x), on the same xy-plane. *Assume the scales of the x-axis and the y-axis are equal.* 2.
3. Application: The magazine Scientific American released a study of data analysis on how quickly children are able to speak in at least single words. Let the function P(t) be the percentage (%) of children who can speak in at least single words by the age of t months old (for 8 <t< 24). Based on the statement P'(14) = 18, you conclude that by the age of percentage of children who can speak in at least single words is increasing/decreasing (circle one) at a rate of months old, the Would you expect P' (t) to increase or decrease, ast increases? Explain your reasoning.
Transcribed Image Text:3. Application: The magazine Scientific American released a study of data analysis on how quickly children are able to speak in at least single words. Let the function P(t) be the percentage (%) of children who can speak in at least single words by the age of t months old (for 8 <t< 24). Based on the statement P'(14) = 18, you conclude that by the age of percentage of children who can speak in at least single words is increasing/decreasing (circle one) at a rate of months old, the Would you expect P' (t) to increase or decrease, ast increases? Explain your reasoning.
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