Question

Question #34c5a

Answer 1

See below.

Explanation:

To find points of inflection we use the first derivative to identify any stationary points. So:

`dy/dx (x^4)=4x^3`

We solve `4x^3=0`

`4x^3=0=>x=0`

We put this value in the second derivative and if the result is `0` then this could be a maximum, minimum or point of inflection.

`(d^2y)/(dx^2) (x^4)=12x^2`

`12(0)^2=0`

To test whether this is a max/min or point of inflection, using the first derivative we test either side of the point and if there is no change in the sign then this is a point of inflection.

Just left of `0` we use `-0.1`

`4(-0.1)^3=-0.004` this is a negative slope \

Just right of `0` we use `0.1`

`4(0.1)^3=0.004` this is a positive slope /

So there is a change in the slope from negative to positive which indicates a minimum value so no point of inflection.

The above may not be entirely true, and is a matter of opinion.

See the comment from Steve M in the comments sections.

Hope this helps.