Finding the Point of Inflection

**Paymemoney** · May 1st 2010, 04:03 PM

Hi

I need help on the following question:

1) Find the exact values of the x-coordinates of the points of inflection on the graph of $y=2x^4+4x^3-x^2+7x-1$

Ok this is what i have done:
$\frac{dy}{dx} = 8x^3 + 12x^2 - 2x +7$

$\frac{d^2y}{dx^2} = 24x^2+24x-2$

make $\frac{d^2y}{dx^2} = 0$

Now i tried using the quadratic equation but the answer i got does not look correct.

Would someone tell me what should i do instead?

P.S

**skeeter** · May 1st 2010, 05:40 PM

Originally Posted by Paymemoney

Hi

I need help on the following question:

1) Find the exact values of the x-coordinates of the points of inflection on the graph of $y=2x^4+4x^3-x^2+7x-1$

Ok this is what i have done:
$\frac{dy}{dx} = 8x^3 + 12x^2 - 2x +7$

$\frac{d^2y}{dx^2} = 24x^2+24x-2$

make $\frac{d^2y}{dx^2} = 0$

Now i tried using the quadratic equation but the answer i got does not look correct.

Would someone tell me what should i do instead?

P.S

$x = \frac{-3 \pm 2\sqrt{3}}{6}$

**Paymemoney** · May 1st 2010, 06:35 PM

i get $\frac{-24+\sqrt{768}}{48}$ and $\frac{-24-\sqrt{768}}{48}$ ?

which value is the POI??

**skeeter** · May 1st 2010, 06:40 PM

Originally Posted by Paymemoney

i get $\frac{-24+\sqrt{768}}{48}$ and $\frac{-24-\sqrt{768}}{48}$ ?

which value is the POI??

both are ... why?

**Paymemoney** · May 1st 2010, 06:49 PM

isn't one of the values a minimum?

**skeeter** · May 1st 2010, 07:06 PM

Originally Posted by Paymemoney

isn't one of the values a minimum?

both inflection points are marked in red ...

**Paymemoney** · May 1st 2010, 07:17 PM

ok, if i was asked to find the minimum how would i find it??

Would i take the derivative again?

**skeeter** · May 1st 2010, 07:26 PM

Originally Posted by Paymemoney

ok, if i was asked to find the minimum how would i find it??

Would i take the derivative again?

minimum will be where the first derivative equals 0 ... you'll need to use a calculator to solve the cubic equation.

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