3. (Applies to Standard D1) This question will be referring to this definitionm of the derivative of a function f at a point a. S(a + h) - f(a) f'(a) = lim The figure shows the graph of a function y = S(r) and a number a marked on the x-axis. (a) Illustrate aud label each of the following quantities that appear in this definition on the graph. (You may assume h > 0.) Then write a short statement explaining in terms of the figure what each quantity means. i. f(a) ii. h iii. f(a + h) iv. la+h)-f(a) f(a + h) - f(a) (b) Explain in terms of tangent and secant lines what the equation f'(a) = lim means. Include an explanation of what the symbol lim means and why it is needed. %3D h-0
3. (Applies to Standard D1) This question will be referring to this definitionm of the derivative of a function f at a point a. S(a + h) - f(a) f'(a) = lim The figure shows the graph of a function y = S(r) and a number a marked on the x-axis. (a) Illustrate aud label each of the following quantities that appear in this definition on the graph. (You may assume h > 0.) Then write a short statement explaining in terms of the figure what each quantity means. i. f(a) ii. h iii. f(a + h) iv. la+h)-f(a) f(a + h) - f(a) (b) Explain in terms of tangent and secant lines what the equation f'(a) = lim means. Include an explanation of what the symbol lim means and why it is needed. %3D h-0
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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Transcribed Image Text:3. (Applies to Standard D1)
This question will be referring to this definition
of the derivative of a function f at a point a.
S(a + h) – f(a)
f'(a) = lim
The figure shows the graph of a function y =
S(r) and a number a marked on the x-axis.
(a) Illustrate and label eaclh of the following quantities that appear iu this definition on the
graph. (You may assume h > 0.) Then write a short statement explaining in terms of the
figure what each quantity means.
i. f(a)
ii. h
iii. f(a + h)
iv. la+h)-f(a)
f(a + h) – f(a)
(b) Explain in terms of taugent and secant lines what the equation f'(a) = lim:
means. Include an explanation of what the symbol lim means and why it is needed.
h-0
h-0
3
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