Question

A bit of confusion here...

Answer 1

I'm confuse too....there's nothing here @.@

Answer 2

The question is:
Let f be a function with a second derivative given by \[f''(x) = x^2(x - 3)(x - 6)\] What are the x-coordinates of the points of inflection of the graph of f?

Answer 3

I set the equation to 0 to find the inflection points, and I get 0, 3, and 6. But the answers shows that it is only 3 and 6. Why is that?

Answer 4

From wikipedia:
an inflection point, point of inflection, flex, or inflection (inflexion) is a point on a curve at which the curvature or concavity changes sign from plus to minus or from minus to plus.

if we check x=0 by looking at the sign at -dx (a little below 0) and +dx (a little above 0) we see that the sign does not change.

Answer 5

See http://en.wikipedia.org/wiki/Inflection_point

Answer 6

Is there a way to do that w/o a graph or a calculator?

Answer 7

let x= -0.001 in
f''(x) = x^2(x - 3)(x - 6)
the sign will be + * - * - = +
with x= +0.001 the sign is
+ * - * -1 = +
so no sign change in f'' means you do not have an inflection point

Answer 8

I sort of get it. Do i have to make an interval table to do that?

Answer 9

Refer to the attached Mathematica 9 solution.