# 4x^2+4x+1

Input |
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4 x^2 + 4 x + 1 |

Geometric figure |

parabola |

Root |

x = -1/2 |

Polynomial discriminant |

Delta = 0 |

Derivative |

d/dx(4 x^2 + 4 x + 1) = 8 x + 4 |

Indefinite integral |

integral (1 + 4 x + 4 x^2) dx = (4 x^3)/3 + 2 x^2 + x + constant |

Global minimum |

min{4 x^2 + 4 x + 1} = 0 at x = -1/2 |