First derivation is: f ' = 16x^{3} + 12x^{2} - 22x + 2 = 0 |

(This curve is sketched by the red line) |

The solutions of first derivation will give us the extreme points |

which are at: x_{1} = -1.64, x_{2} = 0.1 x_{3} = 0.79 |

In order to find if the points are a maximum or minimum we |

shall find the second derivation: f ''(x) = 48x^{2} + 24x - 22 |

Now substitute each extreme point to the second derivation: |

f '' (x_{1}) = 48 * (-1.64)^{2} + 24 * (-1.64) - 22 = 67.7 |

f '' (x_{2}) = 48 * 0.1^{2} + 24 * 0.1 - 22 = -19.1 |

f '' (x_{2}) = 48 * 0.79^{2} + 24 * 0.79 - 22 = 26.9 |

x_{1} - is a minimum, x_{2} - is a maximum, and x_{3} - is a minimum |