16A-WQ06 - Math 16A March 18, 2006 Final l.(5,5,5,5)...

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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 /—\ wlv 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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This note was uploaded on 12/04/2009 for the course MATH 29325 taught by Professor Zhu during the Spring '09 term at UC Davis.

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16A-WQ06 - Math 16A March 18, 2006 Final l.(5,5,5,5)...

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