Question

Calculus help?

I'm am supposed to write an explanation of the difference between the second derivative test (which is used to determine relative maximums and minimums) and the procedure used to determine inflection points.....
I thought it was the same. Please help?

Answer 1

the first derivative to consider max/min, not second one

Answer 2

http://www.math.hmc.edu/calculus/tutorials/extrema/

Answer 3

second one for concave http://www.math.hmc.edu/calculus/tutorials/secondderiv/

Answer 4

you can see that the inflection is not max/min in the example or the graph.

Answer 5

oh yea, the second one help to find out the relative max/min, too

Answer 6

so how do I am i supposed to write about that?

Answer 7

to me, it should be : the process to figure out inflection point can be done by second derivative directly whereas to find relative max/min by considering the sign of f", we need the critical points from the first derivative/

Answer 8

you see, we must know critical point from the first derivative first, and instead of plug those points into the original one to consider whether they are max or min, we plug them into the second derivative and consider its sign, if it > 0, max, if it <0 min without knowing about the value of it (f (critical point)) We just know that there is a max /min at this point only.

Answer 9

got me? I am so sleepy. have to go to bed now,

Answer 10

This helps very much
Thank you