Quiz #2
Name:
Show all work. No Calculator allowed.
3
(1) Let y   on [1, 7]. Using step size = 2, construct both the graph and the piece-wise
x
defined function for y'. Show your scale clearly.

yappox
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Using Euler’s method find a piecewise
linear approximation of y on [1,7] given
that y (1)  3 . Mark coordinates of the
endpoints of each segment clearly.
yappox
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From your work above, give an estimate of y(3).
Is your estimate larger or smaller than the actual value of y(3)? Explain carefully.
(2)
a.
Given the graphs of y  f ( x) below, sketch the graph of y  f ( x) .
b.
(3)
a.
Given the graphs of y  f ( x) below, sketch the graph of y  f ( x) .
b.
(4) Suppose that f(1) = 2 and f (x) < 3 for all values of x.
a. What can be said about the value of f(3)? Explain you reasoning.
b. What can be said about the value of f(– 1)? Explain you reasoning.