The discussion focuses on determining the constants A and B in the function y = Ax^(1/9) + Bx^(-1/9) to achieve an inflection point at (1, 9). The key equations derived include A + B = 9 and -8A + 10B = 0. The incorrect calculations led to A = -5 and B = 14, highlighting algebraic errors in sign management. Correcting these mistakes is essential for accurate results in calculus problems involving inflection points.
PREREQUISITESStudents studying calculus, particularly those tackling problems related to inflection points and derivatives, as well as educators looking for examples of common algebraic errors in mathematical solutions.
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?