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Estimated Instantaneous Rate Of Change

  1. Oct 18, 2016 #1
    1. The problem statement, all variables and given/known data
    You have to graph f(x) = x3 - 2x2 + x and find where the instantaneous rate of change is positive negative and zero.

    2. Relevant equations


    3. The attempt at a solution
    I factored this and found the zero's to be x= 0 and x = 1. With all this info given I graphed it and realized the EIRC is zero at 1 however it's also at 1/3 but I am unsure of how to obtain 1/3???
     
  2. jcsd
  3. Oct 18, 2016 #2
    The question does not ask for the point where "##f(x)##" is positive, negative and zero, rather it asks for where "the instantaneous rate of change" is positive, negative and zero.
    If ##f(x)## is zero, it does not mean that the instantaneous rate of change is also zero. For example, consider the graph of ##y=x^3-2x^2+1##
    Untitled.png
    Have you learnt about differentiation?
     
  4. Oct 20, 2016 #3
    I understand it now. Thank you for the great visual it helped a lot. As for writing the intervals for where it is positive, negative and zero the teacher said to estimate the values of x.
     
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