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

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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.
 
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You get one more equation from the fact that y = 0 at x = 2.
 
i wouldn't of thought of that.
thank you
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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