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.
Max points and points of inflection are concepts in calculus that represent important points on a function's graph. Max points are the highest points on a function's graph and can be found by taking the derivative and setting it equal to zero. Points of inflection, on the other hand, are points where the concavity of the function changes from positive to negative or vice versa. They can be found by taking the second derivative and setting it equal to zero.
Max points and points of inflection provide information about the behavior of a function. They can help determine the highest or lowest values of a function and identify where the graph changes direction. This information is useful in analyzing the behavior of a function and making predictions about its future values.
Yes, a function can have multiple max points and points of inflection. This depends on the complexity of the function and its behavior. For example, a cubic function can have up to two max points and two points of inflection, while a higher degree polynomial can have more.
Max points can be used to optimize a function by finding the highest or lowest values, which can represent maximum or minimum values in real-life situations. Points of inflection can also be used to optimize a function by identifying where the graph changes direction, which can be useful in determining the most efficient path or strategy.
Yes, a function can have no max points or points of inflection. This would mean that the function is either constantly increasing or constantly decreasing, without changing direction or having a maximum or minimum value. An example of this is a linear function with a slope of zero.