Question

Find the point of inflexion of the curve y=x3-6x2+9x+6/6

Answer 1

Answer:

$x = 2$

Step-by-step explanation:

We know that point of inflexion is that point on the curve which neither have maxima nor have minima.

To find that point on the curve

$y = {x}^{3} - 6 {x}^{2} + 9x + 1 \\ \\ \frac{dy}{dx} = 3 {x}^{2} - 12x + 9 \\ \\ put \: \frac{dy}{dx} = 0 \\ \\ 3 {x}^{2} - 12x + 9 = 0 \\ \\ 3 {x}^{2} - 9x - 3x + 9 = 0 \\ \\ 3x(x - 3) - 3(x - 3) = 0 \\ \\ (x - 3)(3x - 3) = 0 \\ x = 3 \\ \\ or \\ \\ x = 1$

point of inflexion can be 1 or 3.

To check ,follow these steps

$\frac{ {d}^{2}y }{ {dx}^{2} } = 6x - 12$

on putting the value of x=1 and x=3,we don't get d^2y/dx^2=0, Thus these points can't be point of inflexion.

Now, put

$\frac{ {d}^{2} y}{ {dx}^{2} } = 0 \\ \\ 6x - 1 2= 0 \\ \\ x = 2$

Thus x=2 is the point of inflexion.

Hope it helps you.

Answer 2

Answer:

x=2 is the point of inflexion.