Plus Two Maths Notes Chapter 5 Continuity and Differentiability is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 5 Continuity and Differentiability.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Notes |

Chapter | Chapter 5 |

Chapter Name | Continuity and Differentiability |

Category | Kerala Plus Two |

## Kerala Plus Two Maths Notes Chapter 5 Continuity and Differentiability

- If a function is continuous at C then

- If 1’ and g’ are continuous at c, then f+g, f-g, f.g, and k.f are continuous at c.
- Composite of two continuous functions is continuous.
**Theorem:**Every differentiable function is continuous. But every continuous function need not to be differentiable. For eg:

*f*(x) = |x| is continuous at x = o, but it is not dif fermentable at x = 0.

**Standard Results**

does not exist at any integral point.

**Rolles Theorem**

Let f be a real function defined in the closed interval [a, b] such that:

- f is continuous in [a, b]
- f is differentiable in (a, b)
- f(a) = f(b), then there exists at least one point c in (a, b) such that f(c) = o

**Lagrange’s Mean Value Theorem**

Let f be a real function defined in the closed interval [a, b] such that:

- fis continuous in the closed interval [a,b]
- f is differentiable in (a, b), then there exists at least one point c in (a, b) such that
- Second order derivative of y = f(x) is It is also denoted by y
^{11}or f^{11}(x) or y_{2.} - If x and y are parametric functions with parameter t then

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