Points of Inflection
Inflection points are points where the function changes concavity, i.e. from being “concave up” to being “concave down” or vice versa.
The second derivative of a function determines the local maximum or minimum, inflection point values. These can be identified with the help of the below conditions:
- If f”(x) < 0, then the function f(x) has a local maximum at x.
- If f”(x) > 0, then the function f(x) has a local minimum at x.
- If f”(x) = 0, then
- it is not possible to conclude anything about the point x
Second Order Derivatives: Rules , Formula and Examples (Class 12 Maths)
The Second Order Derivative is defined as the derivative of the first derivative of the given function. The first-order derivative at a given point gives us the information about the slope of the tangent at that point or the instantaneous rate of change of a function at that point.
Second-Order Derivative gives us the idea of the shape of the graph of a given function. The second derivative of a function f(x) is usually denoted as f”(x). It is also denoted by D2y or y2 or y” if y = f(x).
Let y = f(x)
Then, dy/dx = f'(x)
If f'(x) is differentiable, we may differentiate (1) again w.r.t x. Then, the left-hand side becomes d/dx(dy/dx) which is called the second order derivative of y w.r.t x.
In this article, we have covered Graphical Representation of Second-Order Derivatives along with formulas, examples and many more.
Table of Content
- Second Order Derivatives Overview
- Second Order Derivatives Examples
- Second-Order Derivatives of a Function in Parametric Form
- Graphical Representation of Second-Order Derivatives
- Concavity of Function
- Concave Down
- Points of Inflection
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