Explanation Given: The function is given as: f ( x ) = x 2 + 25 x Graph: To plot the graph, follow the steps in TI-83 calculator: Step 1: In the TI-83 graphical calculator, press the Y = key. Step 2: Enter the equation of f ( x ) as ( X ^ 2 + 25 ) / X in Y 1 . Step 3: Press the TRACE and Y key. Step 4: Go to WINDOW and set X min = − 20 , X max = 20 , Y min = − 20 , Y max = 20 . Step 5: Click on the TRACE key to obtain the graph. The graph is obtained as follows: The x - and y- intercepts are to be calculated. Since x = 0 is not in the domain of the function because f ( x ) is not defined at that point. So there is no y -intercept. To find the x -intercept, solve f ( x ) = 0 . x 2 + 25 x = 0 2 x 2 + 8 x = 0 x 2 + 25 = 0 x 2 = − 25 Since x 2 is never negative, thus there is no x- intercept. Power rule of differentiation states that if f ( x ) = x n for any number n , then f ′ ( x ) = n x n − 1 . Addition rule of differentiation states that if: f ( x ) = u ( x ) + v ( x ) Then f ′ ( x ) is given by: f ′ ( x ) = u ′ ( x ) + v ′ ( x ) Subtraction rule of differentiation states that if: f ( x ) = u ( x ) − v ( x ) Then f ′ ( x ) is given by: f ′ ( x ) = u ′ ( x ) − v ′ ( x ) To find all the critical points, calculate the first-order derivative of the given function. Use the addition rule and power rule: f ′ ( x ) = d d x ( x 2 + 25 x ) = d d x ( x ) + d d x ( 25 x ) = 1 − 25 x 2 Now put f ′ ( x ) = 0 to find critical points

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ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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Chapter 12.6, Problem 15E

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To graph: The function f(x)=x2+25x and locate the point of inflection and local extrema.

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Chapter 12.6, Problem 14E

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To graph: The function f ( x ) = x 2 + 25 x and locate the point of inflection and local extrema.

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To graph: The function f(x)=x2+25x and locate the point of inflection and local extrema.

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