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by: Hannah Moore

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# Math Notes 201501

Hannah Moore
Clayton State

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Notes on Monday in class.
COURSE
Calculus 1
PROF.
Giovannitti
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
Calculus
KARMA
25 ?

## Popular in Math

This 2 page Class Notes was uploaded by Hannah Moore on Monday March 28, 2016. The Class Notes belongs to 201501 at Clayton State University taught by Giovannitti in Spring 2016. Since its upload, it has received 10 views. For similar materials see Calculus 1 in Math at Clayton State University.

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Date Created: 03/28/16
March 21­25, 2016 Section 3.2  Suppose f’(x) >0 for all x on an open interval I. Suppose x < x i1 I. 2 en f(x) is continuous on  [x1  x2] and it is differentiable on (x 1 x 2  2 x ¿ So by Mean Value Theorem there is c ¿ f( )1f ¿ ' ϵ ( 1x S2)hthen f (c)=¿ Which implies  Thus f(x)< 0 is increasing on I. By similar arguments, we can show that f’(x)< 0 on an open  interval f is decreasing on I. And if f’(x)=0 on an open interval I, then f(x) is constant on I. Theorem If f’(x)= g’(x) on an open interval I, then g(x)= f(x) + c for some constant c. 3 2 Sketch curve y= x ­3x  + 7x­2  Step 1 Find Critical points  ' 2 y =3x −6 x+7 2 (−6) −4 3 )7 )<0 No real roots y’ >0 for all real x So y is increasing 3 2 Find the root for y= x ­3x  + 7x­2  Can we estimate the root? Since y(0)= ­2 y(1)=3 The root is between 0 and I, not a rational root  so we use technology to approximate.  ‘ ‘ ‘ ‘ ‘ ‘ ‘ ¿3x−2 Domainis −∞,∞ ) y x +1 2 3 (x +1 − (x−2 2 )( ) y’(x)=  2 2 x +1 ) −3x +4x+3 −(3x −4x−3) 2 = 2 =  x +1 ) (x +1) 2 Let  3x −4x−3=0 2 ´ 4± √ −4 3 ( )( ) 2± √3 x=  2(3) = 3

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