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anonymous

  • 5 years ago

Find all critical points of: f(x)= 3x^4 - 2x^3 - 12x^2 + 18x and use the second derivative test to classify each as a relative maximum, a relative minimum, or neither. I took the 1st derivative and got: 12x^3 - 6x^2 - 24x +18 but after this I need to find the critical points. Not sure how to do this with all of the x's

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  1. amistre64
    • 5 years ago
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    lets start bt taking out the common factors 12x^3 - 6x^2 - 24x +18 6(2x^3 -x^2 -4x +3) --------------------- 2x^3 -x^2 -4x +3 = 0 now we can use some trial and error techniques but improve out odds by taking the factors of the 1st and last 1, 3 ---- this gives us a "pool" of options to limit our search. 1, 2 you can try regular long division, but the synthetic divisioj is more compact: -- ----------- x=1 | 2 -1 -4 3 0 2 1 -3 ------------- 2 1 -3 0 <--remainder 0, its good. I got lucky onthat one :) (x-1) ( 2x^2 +x -3 ) the new expression there can be fatored easily into: (x-1)(x+3)(x-2) = 0 x = -3, 1, 2

  2. anonymous
    • 5 years ago
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    ok as far as the factored equation (x-1)(x+3)(x-2)=0. It has been a while since I have done this kind of problem. Need a refresher course. The (x+3)(x-2) should equal the (2x^2 +x -3) shouldn't it?

  3. amistre64
    • 5 years ago
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    you know what, your right lol ..... i forgot about my "2" there in the front to use as a divisor on this....

  4. amistre64
    • 5 years ago
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    (x-1)(x+3/2)(x-2/2) = 0 (x-1)(x+3/2)(x-1) = 0 x = -1 and x = -3/2

  5. amistre64
    • 5 years ago
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    ....x = 1 and x = -3/2 thats my final offer :)

  6. anonymous
    • 5 years ago
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    hey :P

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