Second derivative

sutupidmath

I would like someone to tell me what is the geometric interpretation of the second derivative at a fixed point, or in an interval??

thx

Eighty

If it's positive on an interval, the function is convex there; if it's negative, the function is concave.

theperthvan

Second derivative is the rate of change of the derivative, i.e "how fast is the gradient changing?".
Say the second derivative is 1 at point A and 2 at point B on the same function. Then the gradient (the derivative) is changing faster at point A than point B.

mathwonk

Homework Helper
it measures curvature, or concavity, tells whether it is up or down, and how sharply.

it also determines whether the tangent line is above or below the graph.

Last edited:

Moridin

http://online.math.uh.edu/Math1314/index.htm [Broken]

See section 11.

Last edited by a moderator:

sutupidmath

i guess i already knew this,just did not actually think about it.
However, if this is what i was looking for, i will see later when i think more about it, and if i still have problems i will come back.

Thankyou guys, for giving me some flash back

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving