I'm assuming you meant "at the point (1,9)" not "as (1/9)".Chas3down said:Homework Statement
Determine A and B so that y = Ax^(1/9) + Bx(-1/9) has an inflection point as (1/9)Homework Equations
A + B = 9
The Attempt at a Solution
F' = Ax^(-8/9)/9 - Bx^(-10/9)/9
F'' = -8Ax^(---)/81 + 10Bx^(---)/81
-8A + 10B = 0
A + B = 9
-10(9-A) - 8A = 0
-90 - 18A = 0
A = -90/18
B = 14
But, this is not correct.. I don't understand what I did wrong?
An inflection point problem refers to a mathematical concept in which a function changes from being convex to concave or vice versa. This results in a change in the direction of the function's curvature.
An inflection point can be identified by finding the point where the function's second derivative changes sign from positive to negative or vice versa. This is where the function's curvature changes direction.
Inflection points are important in analyzing the behavior of a function. They can indicate where a function is changing from increasing to decreasing or vice versa, and can also help identify critical points and extrema.
Yes, it is possible for a function to have multiple inflection points. This can occur when a function has multiple changes in curvature, resulting in multiple points where the second derivative changes sign.
Inflection points can be applied in various fields such as economics, physics, and engineering, to analyze and understand the behavior of various phenomena. They can also be used in optimization problems to find the minimum or maximum value of a function.