Problem 213 from reuben brasher example problem in

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Problem 2.13 (From Reuben Brasher, example problem in section) . Suppose that you know that f 0 ( x ) always has a value between - 1 and 1. Show that | f ( x ) - f ( a ) | ≤ | x - a | . (Hint: Use MVT.)
12 MATH 19A
Problem 2.14 (From Reuben Brasher, example problem in section) . Graph y = f ( x ) = x 2 ( x - 2) 2 . (8)
a. Find the y -intercept, if any. b. Find the x -intercepts, if any.
c. Find the vertical asymptotes.
d. Find the horizontal asymptotes.
MATH 19A 13 e. Find out where the graph intersects any horizontal asymptotes. f. Find out where the function is positive and where it is negative.
g. Find out where the function has critical points.
h. Find out where the function is increasing and decreasing.

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