Let 6 x 2 − 8a) Find the average rate of change from -8 to 5.b) Find an equation of the secant line containing (-8, g(-8)) and (5, g(5)).

Question

Let   6      x    2    −  8a) Find the average rate of change from -8 to 5.b) Find an equation of the secant line containing (-8, g(-8)) and (5, g(5)).

Isaias Archer · Accepted Answer

1. The average rate of change of g(x) over the interval [ -8, 5] is             g      (      5      )      −      g      (      −      8      )              5      −      (      −      8      )        =                    6        ⋅        52        –        8            –              6        ⋅        (        −        8        )        2        −        8                    5      −      (      −      8      )        =            150      −      8      –      384      +      8        13    =            −      234        13    =  182. A secant line is a straight line joining two points on a function. Here, the points are ( -8, g (-8)) and ( 5, g(5)) . Now   g  (  −  8  )  =  6  ⋅  (  −  8  )  2  −  8  =  6  ⋅  64  −  8  =  384  −  8  =  376 and   g  (  5  )  =  6  ⋅  52  –  8  =  6  ⋅  35  −  8  =  150  –  8  =  142. Thus, we are required to find the equation of the line connecting the points ( -8, 376) and ( 5, 142). Now, we know that the slope of the line joining the points   (      x    1    ,      y    1    ) and   (      x    2    ,      y    2    ) is                     y        2            −              y        1                            x        2            −              x        1            . Thus, the slope of the required line is             376      −      142              −      8      −      5        =            −      234        13    =  −  18. We also know that the equation of the line joining the points   (      x    1    ,      y    1    ) and   (      x    2    ,      y    2    ) is   y  −      y    1    =  m  (  x  −      x    1    ), where m is its slope. Finally, the equation of the required secant line is   y  −  142  =  −  18  (  x  −  5  ) or   y  −  142  =  −  18  x  +  90, or   y  =  −  18  x  +  90  +  142 , or   y  =  −  18  x  +  232

Let g(x) = 6x^2 - 8. Find the average rate of change from -8 to 5. Find an equation of the secant line containing (-8, g(-8)) and (5, g(5)). The average rate of change from -8 to 5 is .

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