How Do You Find A and B for an Inflection Point in a Function?

[Chas3down]

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?

 

[vela]

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?

I'm assuming you meant "at the point (1,9)" not "as (1/9)".

Check your algebra when solving for A and B. You made a few sign mistakes.