## Example of inflection point - set theory and calculus, Mathematics

Assignment Help:

Need help, Determine the points of inflection on the curve of the function

y = x3

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#### Aliena

2/13/2013 12:24:41 AM

hey try this...

The only possible inflexion points will happen where

(d2y)/( dx2)   = 0

From specified function as:

(dy)/(dx) = 3x2 and (d2y)/( dx2)   = 6x

Equating the second derivative to zero, we include

6x = 0 or x = 0

We test whether the point at that x = 0 is an inflexion point as follows

While x is slightly less than 0, ((d2y)/(dx2)) < 0; it means a downward concavity

While x is slightly larger than 0, ((d2y)/(dx2)) > 0;  it means an upward concavity

Hence we have a point of inflexion at point x = 0 since the concavity of the curve changes as we pass from the left to the right of x = 0