Question:
Does the point of oblique inflection in a polynomial
function equal to when the gradient is the greatest?

Replies:
By "oblique inflection" I assume you mean a point of inflection where the
slope (gradient) is not zero. If this is so it can go either way. With a
graph it's easy to see. Let us see if we can "talk it through". Starting from
left and going right, if a positive gradient (slope) decreases to a non-zero
positive value, then starts to increase again, then the slope has a minimum,
but non-zero positive value at the point of inflection. On the other hand,
again starting from left and moving right, if negative slope decreases to a
smaller but non-zero slope and then starts to become more negative again,
the slope has a maximum, but negative value, at the point of inflection.

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.