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Unformatted text preview: Math 16A March 18, 2006 Final l.(5,5,5,5) Evaluate the following derivatives. DO NOT SIMPLIFY.
a) a(x) = 4x3 — 3x/J:
(b) b(x) = tan(2x3)
, sin(2x)
(c) em) =
cos(x)
\ d — x/ 3 2* (d) (X) — 6 . dy . 2 _
2.(10)F1nd d— if xy +3y+12=0 wheny=4 andx= 2. x 3.( 10) Find the equation of the line tangent to the curve y = 2sin(x) —— 3cos(2x) when x = 0.
4.( 16) Find all values of x such that the graph of y = f(x) = x4 + x3 is: strictly increasing; strictly decreasing; concave up; and concave down. i . . dy
5.( 10) Pat saw the equation xs1n(y) + ycos(x) = 2 and computed;— = 0.6 , when
x x = 2 and y = 1t/2. Assuming Pat's computation of the derivative is correct, estimate y when x = 1.97.
6.( 15) The old farmer up the road, Mr. McDonald, wants your help in designing two identical rectangular pens side by side with a single common side for the least
possible cost. Each pen should have an area of 600 square feet. Fencing on the
outside of the two pens cost $5 per foot and fencing between the pens costs $3 per
foot. To the nearest 0.01 foot, what should be the dimensions of each pen? Page 2 of 10 Math 16A(5) March 18, 2006 Final Dr. Sallee /—\
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w 7.(l 5) Find the value ofx which maximizes X26 if x+ y =10 where x 3 0 and y _>_ 0. 8.(2()) A rotating laser level rotates once every 2
seconds and shines a tiny red spot of light as
it turns. The laser (L) is placed 50 feet
directly west of point A on a long ﬂat wall.
Point B is 50 feet north of point A on the
wall. If you were measuring the speed of the
spot of light at point B, how fast (in feet/sec)
would it appear to be going? 9.(20) The graph of the equation x2 + 4xy + 6 y2 — 30 = 0 generates an ellipse. Find the
largest and smallest values of y that satisfy the equation. l().( l4)An fellow student brings you some data acquired by measuring the force in Gs
(l G = normal force of gravity at surface of the earth) backward on a piece of
equipment in a test of a new braking system as a function of time. He wants to
know how fast the force is changing at 3 seconds. Explain how you would tell
him to approach the problem and why you would do it that way. Sec .1 1.99 6.44107
2.99 0.02065
3.99 4.25864
2.01 —2.82158
3.01 0.01637
4.01 4.3004 Page 3 of 10 ...
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 Spring '09
 Zhu
 Calculus, Derivative, Monotonic function, Convex function

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