110 A y-f(x) y-f(x) (a) 110 C M- P.1.5) EXAMPLE 1 The graph of a function f is given to the left. Use it to sketch the graph of the derivative f'. SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 5 we draw the tangent at P in the figure and . This allows us to plot the point P'( estimate its slope to be about 3/2, so f'( = are horizontal, so the ) on the graph of f' directly beneath P. Repeating this procedure at several points, we get the lower graph shown in the figure. Notice that the tangents at A, B, and derivative is there and the graph of f' crosses the x-axis at the points A', B', and C', directly beneath A, B, and C. Between A and B the tangents have --Select-- slope, so f '(x) is-Select-- there. But between B and C the tangents have --Select-- slope, so f '(x) is --Select-- there. On Our Website Activate Go to Settin
110 A y-f(x) y-f(x) (a) 110 C M- P.1.5) EXAMPLE 1 The graph of a function f is given to the left. Use it to sketch the graph of the derivative f'. SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 5 we draw the tangent at P in the figure and . This allows us to plot the point P'( estimate its slope to be about 3/2, so f'( = are horizontal, so the ) on the graph of f' directly beneath P. Repeating this procedure at several points, we get the lower graph shown in the figure. Notice that the tangents at A, B, and derivative is there and the graph of f' crosses the x-axis at the points A', B', and C', directly beneath A, B, and C. Between A and B the tangents have --Select-- slope, so f '(x) is-Select-- there. But between B and C the tangents have --Select-- slope, so f '(x) is --Select-- there. On Our Website Activate Go to Settin
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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EXAMPLE 1 The graph of a function f is given to the left. Use it to sketch the graph of the derivative f'.
SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the
point (x, f(x)) and estimating its slope. For instance, for x = 5 we draw the tangent at P in the figure and
)
. This allows us to plot the point P'(
estimate its slope to be about 3/2, so f '(
=
.
) on the graph of f' directly beneath P. Repeating this procedure at several points, we
are horizontal, so the
get the lower graph shown in the figure. Notice that the tangents at A, B, and
derivative is
there and the graph of f' crosses the x-axis at the points A', B', and C', directly
beneath A, B, and C. Between A and B the tangents have --Select--- slope, so f '(x) is-Select-- there.
But between B and C the tangents have ---Select--- slope, so f '(x) is --Select-- there.
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