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# Lecture #4 01/12/2015- Business Calc MATH 112

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This 3 page One Day of Notes was uploaded by Nicole Goodfliesh on Tuesday January 27, 2015. The One Day of Notes belongs to MATH 112 at University of Washington taught by Ebru Bekyel in Winter2015. Since its upload, it has received 140 views. For similar materials see Business Calculus in Mathematics (M) at University of Washington.

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Date Created: 01/27/15

MATH 112 Notes Winter 2015 UW Nicole Good iesh 01122015 Lecture 4 959 Product Quotient Rules uxv xu xvxuxvx EX Find the equation of tangent line to y 1 X 1 at x4 X Point Arie4 1 9 412 4 y XX391X121 y X x112 x12x2x 1 y 394 4112 412424 1116116 uxv Xu xvxuxvx VX2 EX Find f X of fX X24 3X7 uXX24 VX3X7 u X2X V X3 X2432X3X7 6X214X3X212 3X72 3X72 EX Find the instantaneous rate of Change of fX X at x1 2X35X1 uXX VX 2X35X1 u x1 V X 6X25 f X 2X35X1 6X25X 2X35X1 6X35X 2X35X12 2X35X12 4X3 1 2X35X12 I I f 1 4 43 1 5 9 So when X Increases from 10 by 1 un1tfx 2 1 1 DZ 3 6 will increase by approximately 536 MATH 112 Notes Winter 2015 UW Nicole Good iesh EX Compute f X if fX X21 X THERE ARE 3 WAYS 1 Simplify and Differentiate fX X2 l XX391 X X f X 11X391391 1 1 X2 2 Quotient Rule uX X21 VX X u X2X VX1 f X ZXZ X21 X21 1 X2 X2 3 Product Rule fXl X21lX391l xN H uX X21 VX X391 u X 2X V XX392 f X x21x2x12x 2x21 211 11 X2 X2 5 If you have a quotient and the denominator is a number don t use the quotient rule because you can just pull the number out it will still work of course but this is less work EXfXX24X1 1X24X1 1 1 f X 12X4X 13 Application with Cost Revenue Profit CX 00175X32625X250X100 RX4OX What is profit PX 4OX 00175X32625X250X100 MR MRX R X 40 MC MCX C X 00525X2 525X55 MP MPX P X or MRXMCX 4OO0525X2525X55 0025X2525X15 a Find Interval where PX is decreasing 9 Lets find the zeros of the P X function a 0025 b 525 c P X 0025X2525X15 MATH 112 Notes Winter 2015 UW Nicole Good iesh 525525240025153 294 or 9706 20025 9 The red arrows indicate 294 0 9706 0 where p x is decreasing I I p XltO when OSXSZ94Xgt9706 I b Find Interval where PX is increasing 9 Lets find in between the zeros of the P X function I p XgtO when 294ltXlt97O6 I c Find the q where MPO 9 Lets look at where it crosses the X axis I MPO when x2949706 I Summarize 0 294 9706 i i i A b 7 Inc b 9 Sell 97 Units to maximize profit

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