# How do you find all points of inflection given #y=x^5-2x^3#?

##### 1 Answer

Nov 10, 2016

There is just one point of inflection at the origin

#### Explanation:

# y = x^5 - 2x^3 #

Differentiating wrt

# dy/dx = 5x^4 - 6x^2 #

At a critical point ,

So, Either

So critical points occurs when

Next we can find the nature of th critical points by looking at the second derivative:

# dy/dx = 5x^4 - 6x^2 #

# :. (d^2y)/(dx^2) = 20x^3 - 12x #

# :. (d^2y)/(dx^2) = 4x(5x^2 - 3) #

When

So therei is one point of inflection when