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# Quant Analysis MATH 1100

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This 8 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 1100 at University of Utah taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/229932/math-1100-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

Section 93 The Derivative Math 1100 Spring 2009 Interpretations of the Derivative Given a function fz each of the following are different ways to interpret the derivative of 1 Ht 2 derivative of f at z c 3 instantaneous rate of change of f at z c 4 slope of the tangent line to f at z 0 Applications of Derivatives 1 The derivative of a position function gives the velocity function 2 The derivative of a revenue function gives the marginal revenue function 3 The derivative of a cost function gives the marginal cost function 4 The derivative of a pro t function gives the marginal pro t function Math 11005 Fall 2004 Name Derivative Practice Instructions Compute the following derivatives or derivative applications using the techniques and rules devel oped in class Recall the rule of thumb simplify only When needed or for clarity 1 161 1325123 4 rtt214 7t1 2i Vziirl 5i zz2413 3 glttgt 6 fz 7 gt t1t2 54 10 3t t34 52 8 W 21M 11 WC 102 1 5 9 91 12 Suppose the revenue function for a product is given by Rm 1521 11 301 715 Where I is in the thousands of units7 and R is the thousands of dollars made a Find the marginal revenue When 2000 units are sold b How is the revenue Changing When 2000 units are sold 13 Find all points 17y Where the slope of the tangent for I2 7 43 12 is 0 14 Given that 91 5 7 31 7 12437 nd all 1 values for Which f I 0 f I gt 0 fI lt 07 and determine values I Where the function is increasing and Where it is decreasing 15 Write the equation of the tangent line at z 3 for 7 1 y r223 Cometwe kagj fzptwglM W 1 mqu Wm r MK LdILGanA VA WSW M e 019 wwm g 34 MM mm WW 45500 43 r 292 1 Summary of Compound Interest Formulas Let P be the amount deposited t the number of years A the balance r the annual interest rate in decimal form nt 1 Compounded n times per year A P1 5 2 Compounded continuously A x Fequot Find the balance in an account if 2000 is deposited for 10 years at an inter st of 9 compounded as follows Compare the results and make a general tatement about Compounding g a quarterly b monthly i i o daily d continuously AOK WM 0 MamML rub A03 3 Eon Lm arcwclll v39i EXAMPLE 4 Finding the Effective Rate of Interest Find the effective rate of interest corresponding to a nominal rate of 6 per year compounded a annually b quarterly and e monthly YI39I39S x much money should be deposited in an account paying 6 interest impounded monthly in order to have a balance of 20000 after 3 years WWW 0 Exwlxh LLQ f 1TH Q lbx 6 A kma W M650 IfU s It lof gm AX L 433 wax 9k 039 o f ml A M 0Lquot W 5 o D mtm 3 392X 63 41m 36 M 90 26 Q in XZQX 2U 32 319 gt36 y a 7 QM x my 92

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