Unformatted text preview: Department of Mathematics, University of California, Berkeley
Math 16A Alan Weinstein, Fall 1995
First Midterm Exam, Monday, October 2, 1995 Instructions. BE SURE TO WRITE YOUR NAME AND YOUR TA’S NAME AND
SECTION NUMBER ON YOUR BLUE BOOK. Read the problems very carefully to be
sure that you understand the statements. All work should be shown in the blue book;
writing should be legible and clear, and there should be enough work shown to justify your
answers. Indicate the ﬁnal answers to problems by’ circling them. [Point values of
problems are in square brackets. The total point value is 45, for 15% of your course grade] 1. [10 points]
a. Find (1 2 r
370” + (11+ g). b. Find the slope of the curve y = z‘ + 3:1:2 + 246897531 at z = 2. c. Find f’(z) if f(z) = \/1  2:2. Express your answer without using fractional or negative
exponents. 2. [7 points] Write a complete sentence which expresses clearly and precisely the relationship
between derivatives and slopes. 3. [7 points] The number of people riding BART each weekday from Berkeley to the Powell
Street station in San Francisco is thought to be a function f(z) of the fare z, expressed
in cents. Currently, there are 3,500 riders daily at a fare of $1.85. It is believed that
f’ (185) = —50. Bsed on the information above, ﬁnd the best estimate of the daily number
of riders if the fare were raised to $1.90. 4. [6 points]
a. Find b. Find PLEASE TURN THE PAPER OVER FOR THE LAST TWO PROBLEMS. ...
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