Explanation Given: The function is: f ( x ) = x e − x / 2 . Graph: Steps of TI-83 calculator to plot the graph are provided below. Step 1: In the TI-83 calculator, press the [ Y = ] key. Step 2: Enter the equation of f ( x ) as X e ^ ( − X / 2 ) in Y 1 . Step 3: Press the [WINDOW] key and set the widow as: X min = − 2 X max = 9 X scl = 1 . And, Y min = − 2 Y max = 2 Y scl = 1 Step 4: Click the [TRACE] key to obtain the graph. The graph is obtained as follows: To find the y -intercept, set x = 0 in f ( x ) . f ( 0 ) = 0 ⋅ e − 0 / 2 = 0 So, the y -intercept is 0. To find the x -intercepts, solve f ( x ) = 0 . x e − x / 2 = 0 x e x / 2 = 0 x = 0 So, the x- intercept is 0. To find all the critical points, calculate the first order derivative of f ( x ) . f ′ ( x ) = d d x ( x e − x / 2 ) = d ( x ) d x ⋅ e − x / 2 + d ( e − x / 2 ) d x ⋅ x = ( 1 ) ⋅ e − x / 2 + e − x / 2 ( − 1 2 ) ⋅ x = e − x / 2 ( 1 − x 2 ) Now put f ′ ( x ) = 0 to find critical points: e − x / 2 ( 1 − x 2 ) = 0 x = 2 Now find the second order derivative of the function, f ″ ( x ) = d d x ( e − x / 2 ( 1 − x 2 ) ) = d ( e − x / 2 ) d x ⋅ ( 1 − x 2 ) + d ( 1

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ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12.6, Problem 22E

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To graph: The function, f(x)=xe−x/2 and locate the local extrema and inflection points.

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Chapter 12.6, Problem 21E

Chapter 12.6, Problem 23E

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Chapter 12 Solutions

MATHEMATICS WITH APPL....-ACCESS

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To graph: The function, f ( x ) = x e − x / 2 and locate the local extrema and inflection points.

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To graph: The function, f(x)=xe−x/2 and locate the local extrema and inflection points.

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Chapter 12 Solutions