Question

What are inflection points and how do you find them?

Answer 1

i believe you take the second derivative. when there is a sudden change from + to - then there is an inflection point...i believe this happens in cubic functions

Answer 2

does that help? :)

Answer 3

1) Set the second derivative equal to zero 2) Solve for x and those give you the inflection points

Answer 4

Inflection points are found by finding the zeros of the second derivative.

f(x) = x^3 -12x
f'(x) = 3x^2 -12
f''(x) = 6x

Set f''(x) = 0
6x = 0
x = 0

In order for x = 0 to be an inflection point, f''(x) must change signs.
When x < 0, then f''(x) < 0 (You can find this out by testing a number less than 0 in the second derivative).
When x > 0, then f''(x) > 0 (again you can use a test point to find this out).
Since f''(x) changes signs at x = 0, then that is an inflection point.
To find the second coordinate of the point, simply plug in x=0 into f(x).
f(0) = (0)^3 -12(0)
= 0 - 0
= 0
So the inflection point is (0,0).

now,u can depend on it on how to solve,,this is an example :)