To determine To graph: The function f ( x ) = x 1 + x and locate the point of inflection and local extrema. Explanation Given: The function is given as: f ( x ) = x 1 + x Graph: To plot the graph, the steps to be followed in TI-83 are as follows: Step 1: In the TI-83 graphical calculator, press the Y = key. Step 2: Enter the equation of f ( x ) as X / ( 1 + X ) in Y 1 . Step 3: Press the TRACE option and Y key. Step 4: Go to WINDOW and set: X min = − 6 , X max = 6 , Y min = − 6 , Y max = 6 Step 5: Click the TRACE key to obtain the graph. The graph is obtained as follows: The x - and y- intercepts are calculated as: The y -intercept is obtained as: f ( 0 ) = 0 1 + 0 f ( 0 ) = 0 To find the x -intercepts, solve f ( x ) = 0 . x 1 + x = 0 x = 0 So x = 0 is the x -intercept and y = 0 is the y -intercept. Power rule of differentiation states that if f ( x ) = x n for any number n , then f ′ ( x ) = n x n − 1 . Division rule of differentiation states that if: f ( x ) = u ( x ) v ( x ) Then f ′ ( x ) is given by: f ′ ( x ) = u ′ ( x ) ⋅ v ( x ) − u ( x ) ⋅ v ′ ( x ) v ( x ) 2 To find all the critical points, calculate the first-order derivative of the given function: f ′ ( x ) = d

12th Edition

ISBN: 9780134776323

Author: MULLINS

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 12.6, Problem 18E

To determine

To graph: The function f(x)=x1+x and locate the point of inflection and local extrema.

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Chapter 12.6, Problem 17E

Chapter 12.6, Problem 19E

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