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Hw 6 - HW 6(Sec 4.5-5.3 Math 1325 Spring 2010 Calculus with...

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HW 6 (Sec. 4.5-5.3) Math 1325 Spring 2010 Calculus with Applications I Due on: 3/31 Name Instructions: Please solve the following problems . If necessary, come to me for help during my o¢ ce hours. Derivatives of Logarithmic Functions (Section 4.5) : 1. Find the derivative for the following functions. Simplify your answers. ° f ( x ) = ± 5 x 2 ln (3 x ± 2) f 0 ( x ) = d dx ° ± 5 x 2 ln (3 x ± 2) ± = ° f ( x ) = ln ° 2 x 2 + x ± 1 ± 2 = 3 f 0 ( x ) = d dx ² ln ° 2 x 2 + x ± 1 ± 2 = 3 ³ = ° f ( x ) = 5 ln x 2 x 2 ° 1 f 0 ( x ) = d dx ² 5 ln x 2 x 2 ° 1 ³ = 1
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° f ( x ) = log 3 p 2 x ± 3 f 0 ( x ) = d dx ° log 3 p 2 x ± 3 ± = ° f ( x ) = ln ² x ° 1 x +1 ³ f 0 ( x ) = d dx ² ln ² x ° 1 x +1 ³³ = ° f ( x ) = e 2 x ° 1 ln (2 x ± 1) f 0 ( x ) = d dx ° e 2 x ° 1 ln (2 x ± 1) ± = ° f ( x ) = ° e 2 x + ln 3 x ± 3 f 0 ( x ) = d dx ² ° e 2 x + ln 3 x ± 3 ³ = 2
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Increasing and Decreasing Functions and Relative Maximum or Minimum (Section 5.1, 5.2) : 3. For the following function given by: f ( x ) = 8 < : x 2 ± 2 if x < 0 2 ( x ± 1) 3 if 0 ² x ² 2 ± ( x ± 3) 2 + 4 if 2 < x and whose graph is shown below -2 -1 1 2 3 4 -4 -2 2 4 x y y = f ( x ) a) Find critical numbers: b) Find open intervals where: ° f 0 ( x ) > 0 The slope of the tangent line at each point x is the value of f 0 ( x ) : Since we asking for all points where f 0 ( x ) > 0 we need to locate all points where the slope of the tangent line is positive. This holds for the points in the following interval: ° f 0 ( x ) < 0 The slope of the tangent line at each point x is the value of f 0 ( x ) : Since we asking for all points where f 0 ( x ) < 0 we need to locate all points where the slope of the tangent line is negative. This holds for the points in the following interval: c) Find open intervals where: ° f is increasing ( % ) 3
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° f is decreasing ( & ) d) Summarize the results of ( a ) ± ( c ) in the table: x f 0 ( x ) f ( x )
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