Consider the following. f(x) = (x² + 6x + 9) (x-3) (a) Find the derivative of the function, and check your work by graphing both your calculated derivative and the numerical derivative of the function. f'(x) = (b) Use your graph of the derivative to find points where the original function has horizontal tangent lines. (Enter your answers as a comma-separated list.) (c) Use a graphing calculator to graph the function and indicate the points found in part (b) on the graph. y y y 40H 40 40K 20 20 J V N Y X X X -5 5 -5 5 5 -20 -20 -20 -40 -40 -40- -40k X Ⓡ
Consider the following. f(x) = (x² + 6x + 9) (x-3) (a) Find the derivative of the function, and check your work by graphing both your calculated derivative and the numerical derivative of the function. f'(x) = (b) Use your graph of the derivative to find points where the original function has horizontal tangent lines. (Enter your answers as a comma-separated list.) (c) Use a graphing calculator to graph the function and indicate the points found in part (b) on the graph. y y y 40H 40 40K 20 20 J V N Y X X X -5 5 -5 5 5 -20 -20 -20 -40 -40 -40- -40k X Ⓡ
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 following.
f(x) = (x² + 6x + 9) (x − 3)
(a) Find the derivative of the function, and check your work by graphing both your calculated derivative and the numerical derivative of the function.
f'(x) =
(b) Use your graph of the derivative to find points where the original function has horizontal tangent lines. (Enter your answers as a comma-separated list.)
x =
(c) Use a graphing calculator to graph the function and indicate the points found in part (b) on the graph.
y
y
y
40
40
40
40+
20
20
20
20
J K N Y
NY
X
5
-5
-5
5
-5
5
-5
-201
- 20
-20
- 20
-40
- 40
- 40
-40
X
y
5
X
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