f ( x ) = 2 − 3 x 2 ; x = 3 , x = 3 + ha) Determine the net change between the given values of the variable.b) Determine the average rate of change between the given values of the variable.

Question

f  (  x  )  =  2  −  3      x    2    ;  x  =  3  ,  x  =  3  +  ha) Determine the net change between the given values of the variable.b) Determine the average rate of change between the given values of the variable.

ambivalentnoe1 · Accepted Answer

Step 1  f  (  x  )  =  2  −  3      x    2  interval   =  [  3  ,  3  +  4  ]Net change:change in function f(x) for interval [a,b]is given   f  (  b  )  −  f  (  a  )here   a  =  3  ;  b  =  3  +  4So, net change   =  [  2  −  3  (  3  +  4      )    2    ]  −  [  2  −  3  (  3      )    2    ]  =  2  −  3  (  9  +      4    2    +  6  x  )  −  2  +  3  ×  9  =            ⧸            2    −            ⧸            27    −  3      h    2    −  18  h  −            ⧸            2    +            ⧸            2    7  =  −  3      h    2    −  18  hStep 2Avg. rate of change between interval  =  f  (  b  )  −  f  (  a  )      /    b  −  aHere   f  (  b  )  −  f  (  a  )  =  −  3      h    2    −  18  hSo, avg. rate of change   =            −      3              h        2            −      18      h                                ⧸                            3            +      h      −                        ⧸                            3              =                              ⧸                            h            (      −      3      h      −      18      )                                ⧸                            h              =  −  3  h  −  18

f(x)-2-3x^2; X=3, X=3+h. (a) Determine The Net Change Between The Given Values Of The Variable

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