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Note for MATH 115B with Professor Bridges at UA

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15
Bridges ClaskuiDerLSoludocX Math 115b CLASSWORK ON DERIVATIVES 1 Let i Use the de nition of the derivative with h 0001 to calculate f396 to 3 decimal places NOTES YOUR FINAL ANSWER MUST BE ACCURATE TO 3 DECIMAL PLACES SO KEEP AT LEAST 6 DECIMAL PLACES IN THE INNER WORKINGS OF THIS PROBLEM SHOW ALL WORK fxhfx h fxT as h gt0 Let h 0001 and let x 6 f6 0001 f6 0001 f 6 2 0001 6001 5999 211 gt f gt 0002 4 r 4 6001 4 5999 f 6 0002 I 04 997501 0500250 f 6 0002 6 00005125 f 0002 f 6 0 250 2 Let Pc 71663 003s2 245 a Use the short cut to nd P C P c 716 362 003 2c P c 2148c2 006c b Calculate P 3 t02decimal places SHOW WORK P 3 2148 32 006 3 P 3 19314 2 L 1A 3 Let A gm 2 nm73 Use the short cut to nd E M 4 3 7 m n39m 43 1M 3 3 Bridges ClaskuiDeri7Soludocx Math 115b 4 Find the equation ofthe line tangent to y 3x2 7x 9 at x 2 SHOW ALL WORK 1 Find dydX and evaluate at X 2 dy 6 7 dx x dy x2 627 5 dx All straight function lines have the form y mx b We have now found that the slope of our tangent line is m 5 2 Find the point of tangency at x2 y 322 72 9 y 12 14 9 y 7 The point of tangency is 2 7 this means that when x 2 and y 77 3 Find the value of b in y mx b at x 2 ymxb 7 52b 7 10b 3b 4 Finally write the equation of the tangent line y 5x 3 5 Let My 4 y3 2y 1 and let Qy 5My y2 Find the value of QI 3 SHOWALLWORK 1 First nd Qy Qy 5 My 2y Evaluate when y 73 QI 3 5 M 3 6 2 Now nd M I y and evaluate when y 73 My 12y2 2 M 3 12 32 2 M 3 110 3 Substitute this value for M I 3 into the formula for Q 3 Q 3 5 M 3 6 Q 3 5 110 6 Q 3 556 NOTE THERE ARE SEVERAL WAYS TO DO THIS PROBLEM ANOTHER WAY WOULD BE TO FIRST SUBSTITUTE THE EQUATION INTO THE Q y EQUATION AND THEN FIND THE DERIVATIVE OF THE RESULT Bridges C1asku7Deri7SoludocX Math 115b 6 You have discovered that the demand function for your project is Dq 000030312q2 001090045q 29994368909 21 Find the function MDq MDq 000030312 2 q 001090045 MDq 0 00060624q 0 01090045 b Find the function Rq Rq 000030312q3 001090045q2 299 94368909q c Find the function MRq MRq 000030312 3 q2 001090045 2 q 29994368909 MRq 000090936q2 002180090q 299 94368909

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