Hw 6 - 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

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Unformatted text preview: 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 ( x ) = d dx & ¡ 5 x 2 ln (3 x ¡ 2) ¡ = & f ( x ) = ln & 2 x 2 + x ¡ 1 ¡ 2 = 3 f ( x ) = d dx ¢ ln & 2 x 2 + x ¡ 1 ¡ 2 = 3 £ = & f ( x ) = 5 ln x 2 x 2 & 1 f ( x ) = d dx ¢ 5 ln x 2 x 2 & 1 £ = 1 & f ( x ) = log 3 p 2 x ¡ 3 f ( x ) = d dx & log 3 p 2 x ¡ 3 ¡ = & f ( x ) = ln ¢ x & 1 x +1 £ f ( x ) = d dx ¢ ln ¢ x & 1 x +1 ££ = & f ( x ) = e 2 x & 1 ln (2 x ¡ 1) f ( x ) = d dx & e 2 x & 1 ln (2 x ¡ 1) ¡ = & f ( x ) = & e 2 x + ln 3 x ¡ 3 f ( x ) = d dx ¢ & e 2 x + ln 3 x ¡ 3 £ = 2 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 < 2 ( x & 1) 3 if ¡ x ¡ 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 ( x ) > The slope of the tangent line at each point x is the value of f ( x ) : Since we asking for all points where f ( x ) > 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 ( x ) < The slope of the tangent line at each point x is the value of f ( x ) : Since we asking for all points where f ( x ) < 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 & f is decreasing ( ¡ ) d) Summarize the results of ( a ) ¢ ( c ) in the table: x f ( x ) f ( x ) 4. For the following function given by:...
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This note was uploaded on 02/09/2011 for the course BA 2301 taught by Professor Mattpolze during the Spring '08 term at University of Texas at Dallas, Richardson.

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Hw 6 - 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

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