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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
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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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets 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 :) (x1) ( 2x^2 +x 3 ) the new expression there can be fatored easily into: (x1)(x+3)(x2) = 0 x = 3, 1, 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok as far as the factored equation (x1)(x+3)(x2)=0. It has been a while since I have done this kind of problem. Need a refresher course. The (x+3)(x2) should equal the (2x^2 +x 3) shouldn't it?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you know what, your right lol ..... i forgot about my "2" there in the front to use as a divisor on this....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x1)(x+3/2)(x2/2) = 0 (x1)(x+3/2)(x1) = 0 x = 1 and x = 3/2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0....x = 1 and x = 3/2 thats my final offer :)
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