Coupon Accepted Successfully!


Point of Inflection

Consider function f(x) = x3. At x = 0, f′(x) = 0. Also f′′(x) = 0 at x = 0. Such point is called point of inflection, where the second derivative is zero or changes its sign. Consider another function f(x) = sin x. f′′(x) = –sin x. Now f′′(x) = 0 when x = nπ, then these points are called points of inflection.
At point of inflection:
  1. It is not necessary that the first derivative is zero.
  2. Second derivative must be zero or the second derivative changes sign in the neighborhood of point of inflection.
  3. Graph of curve changes its concavity.
  4. If f′′(x) > 0, graph is concave towards negative y-axis and if f′′(x) < 0, graph is concave towards positive y-axis.

Test Your Skills Now!
Take a Quiz now
Reviewer Name