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The graph of a function f is given to the below. Use it to sketch the graph of the derivative f'. y = f(x) 1- SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 3 we draw a tangent at P in the figqure below and estimate its slope to be about – (We have drawn a triangle to help estimate the slope.) Thus f'(3), rounded to two decimal places, is approximately .6 and this allows us to plot the point, with coordinates rounded to two decimal places, P( on the graph f' directly beneath P. (The slope of the graph of f becomes the y-value on the graph of f'.)

The graph of a function f is given to the below. Use it to sketch the graph of the derivative f'. y = f(x) 1- SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 3 we draw a tangent at P in the figqure below and estimate its slope to be about – (We have drawn a triangle to help estimate the slope.) Thus f'(3), rounded to two decimal places, is approximately .6 and this allows us to plot the point, with coordinates rounded to two decimal places, P( on the graph f' directly beneath P. (The slope of the graph of f becomes the y-value on the graph of f'.)

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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The graph of a function f is given to the below. Use it to sketch the graph of the derivative f'. y. y = f(x) SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 3 we draw a tangent 2 (We have drawn a triangle to help estimate the slope.) Thus f'(3), rounded to two decimal places, is 3 at P in the figure below and estimate its slope to be about - approximately .6 and this allows us to plot the point, with coordinates rounded to two decimal places, P'| on the graph f' directly beneath P. (The slope of the graph of f becomes the y-value on the graph of f'.)
Transcribed Image Text:The graph of a function f is given to the below. Use it to sketch the graph of the derivative f'. y. y = f(x) SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 3 we draw a tangent 2 (We have drawn a triangle to help estimate the slope.) Thus f'(3), rounded to two decimal places, is 3 at P in the figure below and estimate its slope to be about - approximately .6 and this allows us to plot the point, with coordinates rounded to two decimal places, P'| on the graph f' directly beneath P. (The slope of the graph of f becomes the y-value on the graph of f'.)
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