If f ( x ) = 3 x 3 − k x 2 + x − 7 k, find a number k such that the graph of f contains the point (-1,6).

Question

If   f  (  x  )  =  3      x    3    −  k      x    2    +  x  −  7  k, find a number k such that the graph of f contains the point (-1,6).

Adrienne Harper · Accepted Answer

Given,  f  (  x  )  =  3      x    3    −  k      x    2    +  x  −  7  kand the graph of f contains the point (-1,6)  (  x  ,  y  )  =  (  −  1  ,  6  )    Let   y  =  f  (  x  )Then  y  =  3      x    3    −  k      x    2    +  x  −  7  k    6  =  3  (  −  1      )    3    −  k  (  −  1      )    2    +  (  −  1  )  −  7  k    6  =  −  3  −  k  −  1  −  7  k    6  +  4  =  −  8  k    10  =  −  8  k    k  =            −      10        8      k  =  −      5    4

If f(x)=3x^3-kx^2+x-7x, find a number k such that the graph of f contains the point (-1,6).

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