How to find instantaneous rate of change for x 3 + 2 x 2 + x at x from 1 to 2?

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How to find instantaneous rate of change for       x          3        +  2      x          2        +  x at x from 1 to 2?

odmeravan5c · Accepted Answer

The instantaneous rate of change is the same as taking the derivative. This is defined at a point.We can easily find that function via power rule:  f  (  x  )  =      x          3        +  2      x          2        +  x  ⇒      f    ′    (  x  )  =  3      x          2        +  4  x  +  1I hope it is clear here that the concept of &quot;instantaneous rate of change&quot; from one point to another doesn&#039;t make any sense. However, you can think about the average rate of change very easily. We just do that in the way we&#039;d think: the change in y divided by the change in x. This gives the following:            f      (      2      )      −      f      (      1      )              2      −      1        =      14    1    =  14

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