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## Lecture #1 01/05/2015- Business Calc

by: Nicole Goodfliesh

288

2

3

# Lecture #1 01/05/2015- Business Calc MATH 112

Marketplace > University of Washington > Mathematics (M) > MATH 112 > Lecture 1 01 05 2015 Business Calc
Nicole Goodfliesh
UW
GPA 3.7
Ebru Bekyel

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This is day one of business calculus where we learned about derivatives.
COURSE
PROF.
Ebru Bekyel
TYPE
One Day of Notes
PAGES
3
WORDS
CONCEPTS
KARMA
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## Popular in Mathematics (M)

This 3 page One Day of Notes was uploaded by Nicole Goodfliesh on Thursday January 22, 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 288 views. For similar materials see Business Calculus in Mathematics (M) at University of Washington.

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Date Created: 01/22/15
MATH 112 Notes Winter 2015 UW Nicole Good iesh 01052015 Lecture 1 93 9 Rates of Change and Derivatives 1 The temperature of an object is given by ft46tt2 t9minutes 0 f9 C What is the Average rate of change AtempAtime of temperature from t2 t0 t10 4610102 9 460100 360 46222 9 924 88 36088 272 34 Cmin 102 8 IThe average rate of change from t2 to t10 is 34 C min I 2 If the distance of a car is given by 320 6320 4180 180 2120 120 2 4 6 What is the average speed rate of change of distance of the car from t2 to t 6 hours 2120 6320 320160 200 50 mileshr 62 4 I The average speed of the car from t2 to t 6 hours is 50 miles hr I In general the average rate of change of fx from xa to xb is flb lfla On a graph it is the slope of the secant line through the 2 points ba MATH 112 Notes Winter 2015 UW Nicole Good iesh 3 Can we compute the speed at ta Problem at an instant there is no time elapse so there is no distance travelled and therefore no speed Big Idea Compute the velocity speed at a tiny interval ex 0001 milliseconds Ex Distance travelled is given by ft2t25t What is the speed at t3 f3hf3 23h253h 23253 3h 3 h 296hh2155h 1815 h 1 12h2h2gz5hgz gg 2h217h 2h17 h h h 2h7 1 19 6 Eventually it becomes closer and 01 172 closer to 17 as h approaches zero 001 1702 0001 17002 I So the speed at t3 is 17 mileshour I In general if you want to find the instantaneous rate of change of f at X you compute fXhfx fxhfx XhX h 9 Simplify until the denominator disappears then plug in h0 lim f X fl Xh jfl X 6 This is called the derivative offas X90 h X approaches 0 MATH 112 Notes Winter 2015 UW Nicole Good iesh When given fx to compute f 2 you can do one of two things 1 Plug in numbers and solve this is the long way lim f x f2hf2 x90 h Simplify and plug in h0 see example 3 above 2 Compute f x with and arbitrary number and then you can plug in any number you want Using 2t2 St for example First take the numerator and solve fxhfx 2th2 5th 2t25t 2t22thh2 225h2t2 1 4th2h25h2Xf 2h24th5h h2h4t5 pull out an h it then cancels with the h in the denominator 2h4t5 9 Plug in h0 204t5 4t5 I f t 4t5 I Then find f 2 by plugging in 2 to this equation so f 2 425 13 9 You can also plug in any number Examples f 0 405 5 f 3 435 17

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