# 4x^2-x-3

Input |
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4 x^2 – x – 3 |

Geometric figure |

parabola |

Polynomial discriminant |

Delta = 49 |

Derivative |

d/dx(4 x^2 – x – 3) = 8 x – 1 |

Indefinite integral |

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

Global minimum |

min{4 x^2 – x – 3} = -49/16 at x = 1/8 |

Definite integral |

integral_(-3/4)^1 (-3 – x + 4 x^2) dx = -343/96~~-3.57292 |

Definite integral area below the axis between the smallest and largest real roots |

integral_(-3/4)^1 (-3 – x + 4 x^2) theta(3 + x – 4 x^2) dx = -343/96~~-3.57292 |