Derivatives |

If a function is continuous at x=c, is it always differentiable at x=c? |

No |

Consider the following function: |

f(x)=-x for all x<0 |

f(x)=x for all x≥0 |

At x=0, the limit from the left (0) equals the limit from the right (0), and the function is continuous. |

But the function it is not differentiable at x=0. |

The graph has a corner at x=0, so a tangent line cannot be drawn there. |

Study Sheet - Derivatives |