ƒ'(x) = lim h→0 f(x + h) − f(x) h The goal of this problem is to break down this definition into pieces and understand their geometric meaning. Consider the diagram below (similar to the first diagram on page 1 of the notes): P(x, f(x)) X y = f(x) Q(x+h, f(x+h)) Horizontal distance (run) Vertical distance (rise) x +h X Match each of the following mathematical expressions with the correct description. Each description should be used once.

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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having trouble with question 1,2,4

f'(x) = lim
h→0
f(x+h)-f(x)
h
The goal of this problem is to break down this definition
into pieces and understand their geometric meaning.
Consider the diagram below (similar to the first diagram
on page 1 of the notes):
P(x, f(x))
X
y = f(x)
Q(x+ h, f(x + h))
Horizontal distance (run)
Vertical distance (rise)
x + h
Match each of the following mathematical expressions
with the correct description. Each description should be
used once.
Transcribed Image Text:f'(x) = lim h→0 f(x+h)-f(x) h The goal of this problem is to break down this definition into pieces and understand their geometric meaning. Consider the diagram below (similar to the first diagram on page 1 of the notes): P(x, f(x)) X y = f(x) Q(x+ h, f(x + h)) Horizontal distance (run) Vertical distance (rise) x + h Match each of the following mathematical expressions with the correct description. Each description should be used once.
1. f(x+h) − f(x) represents
[Select]
2. h represents [Select]
f(x + h) - f(x)
h
3.
B
4. lim
h→0
represents
f(x+h)-f(x)
h
[Select]
represents
Possible descriptions:
A. the slope of the tangent line at the point (x, f(x)).
B. the slope of the secant line joining the points
(x, f(x)) and (x + h, f(x + h)).
C. the vertical distance (the "rise") between the points
(x, f(x)) and (x + h, f(x + h)).
D. the horizontal distance (the "run") between the
points (x, f(x)) and (x + h, f(x + h)).
Transcribed Image Text:1. f(x+h) − f(x) represents [Select] 2. h represents [Select] f(x + h) - f(x) h 3. B 4. lim h→0 represents f(x+h)-f(x) h [Select] represents Possible descriptions: A. the slope of the tangent line at the point (x, f(x)). B. the slope of the secant line joining the points (x, f(x)) and (x + h, f(x + h)). C. the vertical distance (the "rise") between the points (x, f(x)) and (x + h, f(x + h)). D. the horizontal distance (the "run") between the points (x, f(x)) and (x + h, f(x + h)).
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Given that f'x=limh0fx+h-fxh

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