# Thread: Finding the Point of Inflection

1. ## 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 $y=2x^4+4x^3-x^2+7x-1$

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

2. 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

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

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

which value is the POI??

4. 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?

5. isn't one of the values a minimum?

6. Originally Posted by Paymemoney
isn't one of the values a minimum?
both inflection points are marked in red ...

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

Would i take the derivative again?

8. 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.