# Finding the Point of Inflection

• May 1st 2010, 04:03 PM
Paymemoney
Finding the Point of Inflection
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 $\displaystyle y=2x^4+4x^3-x^2+7x-1$

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

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

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

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
• May 1st 2010, 05:40 PM
skeeter
Quote:

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 $\displaystyle y=2x^4+4x^3-x^2+7x-1$

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

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

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

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

$\displaystyle x = \frac{-3 \pm 2\sqrt{3}}{6}$
• May 1st 2010, 06:35 PM
Paymemoney
i get$\displaystyle \frac{-24+\sqrt{768}}{48}$ and$\displaystyle \frac{-24-\sqrt{768}}{48}$?

which value is the POI??
• May 1st 2010, 06:40 PM
skeeter
Quote:

Originally Posted by Paymemoney
i get$\displaystyle \frac{-24+\sqrt{768}}{48}$ and$\displaystyle \frac{-24-\sqrt{768}}{48}$?

which value is the POI??

both are ... why?
• May 1st 2010, 06:49 PM
Paymemoney
isn't one of the values a minimum?
• May 1st 2010, 07:06 PM
skeeter
Quote:

Originally Posted by Paymemoney
isn't one of the values a minimum?

both inflection points are marked in red ...
• May 1st 2010, 07:17 PM
Paymemoney
ok, if i was asked to find the minimum how would i find it??

Would i take the derivative again?
• May 1st 2010, 07:26 PM
skeeter
Quote:

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.