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by: Nicole Goodfliesh

134

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# Lecture #2 01/07/2015-Business Calc MATH 112

Marketplace > University of Washington > Mathematics (M) > MATH 112 > Lecture 2 01 07 2015 Business Calc
Nicole Goodfliesh
UW
GPA 3.7
Ebru Bekyel

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This is from lecture #2 where we learned about Rules of Differentiation.
COURSE
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Ebru Bekyel
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One Day of Notes
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2
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KARMA
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## Popular in Mathematics (M)

This 2 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 134 views. For similar materials see Business Calculus in Mathematics (M) at University of Washington.

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Date Created: 01/22/15
Lecture 2 94 9 Rules of Differentiation e If fxxn then r39 xan1 Exl fx X3 f X 3xquot1 3x2 EXZ fx X f X X14 X0 1 EX3 fx1 which is X0 f X 0 Ex4 fx X which is x12 f X 12X12391 1ZX3912 OR10R1 2x12 ZJX EXS fx 1 which is X39l X f x 1X392 OR1 x2 EX6 fx XH f X l39lx 391 9 The derivative of afx is af x ie leave the coefficients alone Exl fx 3X2 f X 32X2391 6x EXZ fx 5 which is 5X393 X3 f x 53x31 1SX394ORi 15x4 Ex3fx g which is 1 x12 7 7 f x 1 gtlt1121x12 OR 1 7 2 14 14Jx Ex4 fx a constant function f x0 The derivative of any constant is zero 9 ddx fxgx f x g39 x ddx fX gX f 39 X g39 X Exl fx 7x32x25x12 Started with cubic f x 21x24x5 Ended with quadratic Practice 1 fX 3X26X1 a Find f X b Compute derivative at x4 c Find the slope of the tangent line where x4 d Write the equation of the tangent line a f X 32X239160 6x6 I b f 4 646 l18 c Slope of the tangent line at f4 is f 4 so d Slope 18 Point 4 342641 9 4 23 y y1 mX X1 9y2318X 4 I 2 Find the points on y2x33X212x5 where the tangent is horizontal ie Where y 0 y 23x339132x2391120 6X26X12 X1 0 6X26X12 6 On a graph the 26X2X2 tangent lines would 26X1X2 be horizontal at X1 or X22 these points X2 In general I I if f x gt 0 the function is going up increasing if f x lt 0 the function is going down decreasing if f x 0 the function 18 horlzontal

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