Max points, points of inflection

[fitz_calc]

Homework Statement

which best describes y=4x^3 - 3x^4
find max/min points and inflection points

The Attempt at a Solution

When I work this one out I get x<0 and 0<x<1 as my two local max points. However, the book says there is only ONE max point - why is this?

with the second derivative I do get two inflection points of 0 and 1/2 which I assume to be correct.

Thoughts??

 

[rs1n]

I think that you'll see where your mistakes are once you write down a clear definition of an inflection point, and of a local extremum. I'll go ahead and say this (because it's often a step that students forget): did you check that your critical points are in fact local max/min points? Likewise for inflection points.

Can you also post your solution?

 

[HallsofIvy]

Homework Statement

which best describes y=4x^3 - 3x^4
find max/min points and inflection points

The Attempt at a Solution

When I work this one out I get x<0 and 0<x<1 as my two local max points. However, the book says there is only ONE max point - why is this?

That makes no sense at all. Max/min points are individual points, not sets of points. HOW did you "work this one out"? If you mean that you got x= 0 and x= 1 as your max/min points, it is true that the derivative is 0 at x= 0 and x= 1, but that is not enough to be a max or a min.

with the second derivative I do get two inflection points of 0 and 1/2 which I assume to be correct.

That is not at all what I get. What is the second derivative?