TinyBrain From: US Posts: 27 Votes: 81 |
I need to find the relative extrema of the function f(x) =x4 - 6x3+ 3 I am to use the secondderivative if possible. This is a work sheet. I wouldlike to know how to find the relative extrema. |

ProfessorMath5 From: US Posts: 4 Votes: 12 |
F(x) = x4 - 6x3 + 3 f''(x) = 4x3 - 18x2 f'''(x) = 12x2 - 36x Set f''(x) = 0 f''(x) = 4x3 -18x2 = 0 factor out 2x2(2x -9) = 0 2x2 = 0 and 2x - 9 = 0 2x2 = 0 is thrown out 2x - 9 = 0 x = 9/2 x = 4.5 Plug this back into the orginal equation to get they-value f(4.5) = (4.5)4 - 6(4.5)3 + 3 y = -133.6875 Check the sign of the 2nd derivative at x-value 4.5 f'''(4.5) = 12(4.5)2 - 36(4.5) f'''(4.5) = 81 so concave up and therefore relativeminima |

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