Concavity (1 Viewer)

[omgmynameislong]

The point (1.6) lies on the curve y=f(x). If f''(x) = 12(x-1)^2, determine whether (1,6) is a point of inflexion or not.

Subbing in 1 gives 0 for the 2nd derivative but the answer says it isn't a pt of inflexion ?_?...

 

[life92]

The point (1.6) lies on the curve y=f(x). If f''(x) = 12(x-1)^2, determine whether (1,6) is a point of inflexion or not.

Subbing in 1 gives 0 for the 2nd derivative but the answer says it isn't a pt of inflexion ?_?...

Sometimes even if the second derivative is 0 at a certain point it doesn't necessarily mean its an inflexion.

Also Xcelz, that goes for if the first AND second derivative are 0, doesn't necessarily mean its an inflexion.

For example, f(x) = x^4
f'(x) = 4x^3 and f''(x) = 12x^2
If you sub x=0, both the first and second derivatives are 0, but it's only a minimum turning point and NOT an inflexion (as from the graph looks like a parabola).

So what you need to do, is test concavity on both sides of the point to ensure it is an inflexion - this is a fail proof method.

 

[omgmynameislong]

Hahaha completely forgot testing the concavity on both side.