Math 2.0

Real functions Definition

Second derivative

Builds on Higher derivative

Definition

Let II be an open interval and let f ⁣:I→ℝf \colon I \to \mathbb{R} be differentiable on II. If f′f' is differentiable at a∈Ia \in I, the second derivative of ff at aa is f′′(a)=(f′)′(a)f''(a) = (f')'(a).

Remarks

It is the higher derivative f(2)f^{(2)}. Another notation is d2fdx2\frac{d^2 f}{dx^2}. If f′′>0f'' > 0 on II, then ff is convex on II. In mechanics, if f(t)f(t) is the position at time tt, then f′′(t)f''(t) is the acceleration.

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Limit point of a set, definition, no evidence levelLimit point of a setdefinitionLimit of a function, definition, no evidence levelLimit of a functiondefinitionDerivative, definition, no evidence levelDerivativedefinitionDifferentiable function, definition, no evidence levelDifferentiable functi…definitionDerivative function, definition, no evidence levelDerivative functiondefinitionHigher derivative, definition, no evidence levelHigher derivativedefinitionSecond derivative, definition, no evidence levelSecond derivativedefinition
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  1. Limit point of a set definition
  2. Limit of a function definition
  3. Derivative definition
  4. Differentiable function definition
  5. Derivative function definition
  6. Higher derivative definition
  7. Second derivative definition

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8 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Second_derivative, lead section
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