Question

CALCULUS:

How do I find the Inflection point?
http://screencast.com/t/M74UKjB9B5

Answer 1

take the second derivative

Answer 2

and then?

Answer 3

if its negative, its concave down, if its positie its concave up.

Answer 4

or take the first derivative

Answer 5

find when its zero, and check that the left side is the same sign as the right side

Answer 6

Where the second derivative is undefined or 0 we have an inflection point.

Answer 7

But how do I calculate the very inflection point? @ganeshie8 can you give a hand please?

Answer 8

@robtobey @agent0smith

Answer 9

For 15, there won't be an inflection point - the function's second derivative is f'' = 2, which means it's concave up everywhere (since f'' is 2 everywhere).

To find where f is decreasing/increasing, you just want the turning point - find this by getting f' and setting f' = 0 and solving for x. Then pick values to the left and right of that x point, and check the sign of f' at those points. + means increasing, - means decreasing.

Answer 10

Same deal for 16, no inflection point (f'' can never be zero)