Example 12: Sketch a graph of the function f(x) = x² - 4x³ + 10 using the following steps. (a) Identify where the extrema of f occur. (b) Find the intervals on which f is increasing and the intervals on which f is decreasing. (c) Find where the graph of f is concave up and where it is concave down. d) Sketch the general shape of the graph for f. e) Plot some specific points, such as local maximum and minimum points, points of inflection, and intercepts. Then sketch the curve. کوند الب اريم

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Example 12: Sketch a graph of the function f(x) = x¹ − 4x³ + 10
Fran
following steps.
using the
(a) Identify where the e extrema
of f occur.
(b) Find the intervals on which f is increasing and the intervals on which f is decreasing.
(c) Find where the graph of f is concave up and where it is concave down.
(d) Sketch the general shape of the graph for f.
(e) Plot some specific points, such as local maximum and minimum points, points of
inflection, and intercepts. Then sketch the curve.
لم
أريام
المندرا
Transcribed Image Text:Example 12: Sketch a graph of the function f(x) = x¹ − 4x³ + 10 Fran following steps. using the (a) Identify where the e extrema of f occur. (b) Find the intervals on which f is increasing and the intervals on which f is decreasing. (c) Find where the graph of f is concave up and where it is concave down. (d) Sketch the general shape of the graph for f. (e) Plot some specific points, such as local maximum and minimum points, points of inflection, and intercepts. Then sketch the curve. لم أريام المندرا
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