Finding parts of an equation given Inflection point.

[sdunker]

I have no clue how to do this.

Determine the values of a and b so that the function p(x)=ax⁴+bx³ will have a point of inflection at (-1,3). You don't have to write out how to do the whole problem but some direction would be great.

Thanks.

 

[Ishuda]

I have no clue how to do this.

Determine the values of a and b so that the function p(x)=ax⁴+bx³ will have a point of inflection at (-1,3). You don't have to write out how to do the whole problem but some direction would be great.

Thanks.

Use the definition of an inflection point. For example, from
http://en.wikipedia.org/wiki/Inflection_point

A differentiable function has an inflection point at (x, f(x)) if and only if its first derivative, f′, has an isolated extremum at x. (This is not the same as saying that f has an extremum). That is, in some neighborhood, x is the one and only point at which f′ has a (local) minimum or maximum.

So choose a and b so that f' has a maximum or minimum.