Finding the Value of b for a Point of Inflection at (2,0)

[coookiemonste]

Homework Statement

If the graph of y=x^3+ax^2+bx-8 has a point of inflection at (2,0), what is the value of b?
the answer is 8.

Homework Equations

The Attempt at a Solution

y'=3x^2+2ax+b
y''=6x+2a
Let y''=0=6x+2a then i plugged in 2 for x
and got -6=a
So y'=3x^2-12x+b...
I don't know where to go from here.

 

[dx]

You get one more equation from the fact that y = 0 at x = 2.

 

[coookiemonste]

i wouldn't of thought of that.
thank you