Question

How can the second derivative help me find the relative maximum and relative minimum of a function?

Answer 1

Please come i need help http://openstudy.com/study#/updates/54502634e4b0c26d0cb2a905 PLease Explain and HElp

Answer 2

I know the 2nd derivative will help me identify the point of inflection.

Answer 3

so there's this test called the second derivative test
basically if you know an x value makes f' (x) = 0, then it is what we call a critical point
it could be a minimum or a maximum, or neither. The second derivative test tells us which is the case.

So, here's how it works...

Answer 4

you plug the x value into the 2nd derivative
if you get a negative answer, that value of x is a maximum of the function
if you get a positive answer, that x value is a minimum
if you get 0, the test gives you no information

Answer 5

but don't I need to use the first derivative to determine the location of the max or min

Answer 6

yes, the x values that could be min/max you get from the first derivative

Answer 7

then the 2nd derivative can tell you what type of special point those x values you get from the 1st derivative are

Answer 8

ok now I see

Answer 9

Thanks

Answer 10

2nd derivative can also tell you about concavity and inflection points as you mentioned at the beginning

Answer 11

and yw :)

Answer 12

Don't I have to also, make sure that f"(x)=0 as well

Answer 13

only when you're finding inflection points

Answer 14

inflection points occur where the 2nd derivative changes sign
where the graph goes from concave up to concave down or vice versa

Answer 15

but for finding whether a point is min/max, you just see what the value of the 2nd derivative is when you plug that x in

Answer 16

thanks

Answer 17

yw