Please use graph paper to complete this assignment. If needed, here is a sheet of graph paper . y = f(x) hz 1 1. 0 Let's sketch a graph of f' (x). Are you wondering how to get started? Keep in mind that the input- output pairs will be (x, f' (x)), and recall that f'(x) is the slope of the tangent line to the graph of f (x) at x. So for example, looking at the graph we see that f' (1.5) = 0. Why? Because the tangent line to the graph of f(x) is horizontal at x = 1.5, so the slope is mtan = 0. Therefore, (1.5, 0) is a point on the graph of f'(x). Also, if we imagine a tangent line at the point (5, 1) on the graph of f (x), we may estimate mtan = 1.5 at x = 5. So the point (5, 1.5) is also a point on the graph of f'(x). Here's another hint. If the graph of f (x) is decreasing on an interval, then the slopes of the tangent lines to the curve on that interval will be negative. And, if the graph of f(x) is increasing on an interval, the slopes of the tangent lines to the curve on that interval will be positive. O.k. let's sketch that graph. First, identify additional points on the graph of f' (x). Then use graph paper to plot the points and then sketch the graph of f' (x). Be sure to label your graph appropriately.
Please use graph paper to complete this assignment. If needed, here is a sheet of graph paper . y = f(x) hz 1 1. 0 Let's sketch a graph of f' (x). Are you wondering how to get started? Keep in mind that the input- output pairs will be (x, f' (x)), and recall that f'(x) is the slope of the tangent line to the graph of f (x) at x. So for example, looking at the graph we see that f' (1.5) = 0. Why? Because the tangent line to the graph of f(x) is horizontal at x = 1.5, so the slope is mtan = 0. Therefore, (1.5, 0) is a point on the graph of f'(x). Also, if we imagine a tangent line at the point (5, 1) on the graph of f (x), we may estimate mtan = 1.5 at x = 5. So the point (5, 1.5) is also a point on the graph of f'(x). Here's another hint. If the graph of f (x) is decreasing on an interval, then the slopes of the tangent lines to the curve on that interval will be negative. And, if the graph of f(x) is increasing on an interval, the slopes of the tangent lines to the curve on that interval will be positive. O.k. let's sketch that graph. First, identify additional points on the graph of f' (x). Then use graph paper to plot the points and then sketch the graph of f' (x). Be sure to label your graph appropriately.
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:Prompt
Please use graph paper to complete this assignment. If needed, here is a sheet of graph paper .
y
y = f(x)
hz
1
0
X
Let's sketch a graph of f' (x). Are you wondering
how to get started? Keep in mind that the input-
output pairs will be (x, f' (x)), and recall that f'(x)
is the slope of the tangent line to the graph of f(x)
at x.
So for example, looking at the graph we see that
f' (1.5) = 0. Why? Because the tangent line to the
graph of f (x) is horizontal at x = 1.5, so the slope
is mtan
= 0. Therefore, (1.5, 0) is a point on the
graph of f'(x).
Also, if we imagine a tangent line at the point (5, 1) on the graph of f (x), we may estimate mtan = 1.5 at x = 5. So
the point (5, 1.5) is also a point on the graph of f'(x).
Here's another hint. If the graph of f (x) is decreasing on an interval, then the slopes of the tangent lines to the curve
on that interval will be negative. And, if the graph of f (x) is increasing on an interval, the slopes of the tangent lines to
the curve on that interval will be positive.
O.k. let's sketch that graph. First, identify additional points on the graph of f' (x). Then use graph paper to plot the
points and then sketch the graph of f' (x). Be sure to label your graph appropriately.
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