Consider the function f(x) = 4x - x² and the point P(2, 4) on the graph of f. Exercise (a) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. Step 1 To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the function f(x) for various values of x. Consider x = 3. To evaluate f(x) with x = 3, substitute 3 for x In f(x). f(x) = 4x-x² f(3) = 4(3)-(3)² = 3 3.
Consider the function f(x) = 4x - x² and the point P(2, 4) on the graph of f. Exercise (a) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. Step 1 To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the function f(x) for various values of x. Consider x = 3. To evaluate f(x) with x = 3, substitute 3 for x In f(x). f(x) = 4x-x² f(3) = 4(3)-(3)² = 3 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the function f(x) = 4x - x² and the point P(2, 4) on the graph of f.
Exercise (a)
Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5.
Step 1
To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the function f(x) for various values of x.
Consider x = 3. To evaluate f(x) with x = 3, substitute 3 for x In f(x).
f(x) = 4x-x²
f(3) = 4(3) - (3)²
3.
Transcribed Image Text:Exercise (b)
Find the slope each secant line.
Step 1
Recall that the slope of a non-vertical line is a measure of the number of units the line rises (or falls) vertically for each unit of horizontal change from left to right. Thus, the slope of a line passing through P(2, 4) and Q(x, f(x)) is given by
Slope = m =
f(x) - 4
x-2
Submit
2)
x-2
x-2
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x 2.
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