Find points of inflection from f''(x) = 12x + 18? A bit confused

[939]

Homework Statement

In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10.

Homework Equations

f (x) = 2x^3 + 9x^2 - 24x - 10
f'(x) = 6x^2 + 18x - 24
f''(x) = 12x + 18.

The Attempt at a Solution

What I don't get is why it asks for pointS. Isn't there just a single point here? Or can you get them not only by using the second derivative?

I.e., set f"x = 0. Yet here only one point does that, not multiple ones? :S Could it be just a typo in the book?

 

[Mark44]

Homework Statement

In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10.

Homework Equations

f (x) = 2x^3 + 9x^2 - 24x - 10
f'(x) = 6x^2 + 18x - 24
f''(x) = 12x + 18.

The Attempt at a Solution

What I don't get is why it asks for pointS.

They are just asking the question in a general way, to include the possibility of multiple inflection points.

Isn't there just a single point here? Or can you get them not only by using the second derivative?

I.e., set f"x = 0. Yet here only one point does that, not multiple ones? :S Could it be just a typo in the book?

 

[939]

They are just asking the question in a general way, to include the possibility of multiple inflection points.

That's what I was thinking, but why wouldn't they write point(s) or point/points then? . But yea you simply have to be right, I don't see how it's possible to find two from that...

 

[Mark44]

You're blowing a really minor thing way out of proportion. When they say "find the points of inflection ..." the possibilities are

*no such points
*one point
*two or more points

You should find something else to worry about.

 

[939]

You're blowing a really minor thing way out of proportion. When they say "find the points of inflection ..." the possibilities are

*no such points
*one point
*two or more points

You should find something else to worry about.

 

[Ray Vickson]

Homework Statement

In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10.

Homework Equations

f (x) = 2x^3 + 9x^2 - 24x - 10
f'(x) = 6x^2 + 18x - 24
f''(x) = 12x + 18.

The Attempt at a Solution

What I don't get is why it asks for pointS. Isn't there just a single point here? Or can you get them not only by using the second derivative?

I.e., set f"x = 0. Yet here only one point does that, not multiple ones? :S Could it be just a typo in the book?

I think the wording is their way of testing you. If they said inflection "point" that would be giving you a hint that there is only one. By saying "points" they are making you think about it.

RGV