Question

What is the significance of the points found by equating first derivative to the second derivative

Answer 1

second derivative helps to weed out the points of inflection

Answer 2

it also helps to define the concavity of the points

Answer 3

Can you give me an article on a site to study on these points ?

Answer 4

nothing comes to mind. The webpages presented at the bottom of the page are good resources

Answer 5

Ok so the points on inflection of x^3 - x would be 3x^2 - 1 = 6x right ?

Answer 6

is f(x) = x^3 -x ?

Answer 7

yes

Answer 8

the f'(x) = 3x^2-1

3x^2-1 =0 will give us critical points to check; and there doesnt seem to be any value to make it go undetermined ...

Answer 9

3x^2-1 = 0

3x^2 = 1

x^2 = 1/3

x = +- sqrt(1/3) is a point to notice right?

Answer 10

yes i know that but what about the points where the graph changes from convexity to concavitivty..? We get it by equation 1st and 2nd derivative like this right ? 3x^2 - 1 = 6x

Answer 11

no; we get it by finding critical points of f' and f''

Answer 12

f'(x) = 3x^2 -1

f''(x) = 6x

at 6x=0 we have inflection

Answer 13

Ok

Answer 14

f' gives us points that may or maynot be inflections; since an inflection can hide behind an f'=0

but, if f''=0 we have a higher degree of certainty that its an inflection; but the best option is to test it out by noticing if the sign stays the same or changes from left to right

Answer 15

6x = 0 when x = 0

<.........0..........>
- +

sign changes which means concavity changes; it has to be an inflection