The discussion centers on finding the maximum and minimum points, as well as the inflection points, for the function y=4x^3 - 3x^4. The participant initially identifies two local maximum points but is corrected by others who clarify that there is only one maximum point. The confusion arises from the need to verify that critical points are indeed local extrema. The second derivative test reveals two inflection points at x=0 and x=1/2, although there is disagreement regarding the accuracy of this result.
PREREQUISITESStudents studying calculus, particularly those focusing on polynomial functions and their properties, as well as educators seeking to clarify concepts of maxima, minima, and inflection points.
That makes no sense at all. Max/min points are individual points, not sets of points. HOW did you "work this one out"? If you mean that you got x= 0 and x= 1 as your max/min points, it is true that the derivative is 0 at x= 0 and x= 1, but that is not enough to be a max or a min.fitz_calc said:Homework Statement
which best describes y=4x^3 - 3x^4
find max/min points and inflection points
The Attempt at a Solution
When I work this one out I get x<0 and 0<x<1 as my two local max points. However, the book says there is only ONE max point - why is this?
That is not at all what I get. What is the second derivative?with the second derivative I do get two inflection points of 0 and 1/2 which I assume to be correct.