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# Math Notes 201501

Clayton State

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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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