Determine the monotonic intervals of the functionsi need to determine the monotonic intervals of this function y = 2 x 3 − 6 x 2 − 18 x − 7. I tried the below but i am not sure if i am doing it right.My work: y = 2 x 3 − 6 x 2 − 18 x − 7 ⟺ 6 x 2 − 12 x − 18 = 0 ⟺ 6 ( x 2 − 2 x − 3 ) = 0 ⟺ ( x − 3 ) ( x + 1 ) ⟺ x − 3 = 0 x + 1 = 0 ⟺ x = 3 , x = − 1 so my function increases when x ∈ [ 3 , + ∞ [ and decreases when x ∈ [ − 1 , 3 ] ∪ ] − ∞ , − 1 ].Please i want to know how to solve this problem any help with explanation will be appreciated. thanks in advanced

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Determine the monotonic intervals of the functionsi need to determine the monotonic intervals of this function   y  =  2      x    3    −  6      x    2    −  18  x  −  7. I tried the below but i am not sure if i am doing it right.My work:                     y        =        2                  x          3                −        6                  x          2                −        18        x        −        7                            ⟺        6                  x          2                −        12        x        −        18        =        0                                          ⟺        6        (                  x          2                −        2        x        −        3        )        =        0                                          ⟺        (        x        −        3        )        (        x        +        1        )                                          ⟺        x        −        3        =        0        x        +        1        =        0                                          ⟺        x        =        3        ,        x        =        −        1            so my function increases when   x  ∈  [  3  ,  +  ∞  [ and decreases when   x  ∈  [  −  1  ,  3  ]  ∪  ]  −  ∞  ,  −  1  ].Please i want to know how to solve this problem any help with explanation will be appreciated. thanks in advanced

Favatc6 · Accepted Answer

Step 1You have correctly found the derivative             d      y              d      x        =  6      x    2    −  12  x  −  18  =  6  (      x    2    −  2  x  −  3  )  =  6  (  x  −  3  )  (  x  +  1  ) and where it is zero, but you have not quite got the intervals correct.The derivatives is positive if and only if   (  x  −  3  )  (  x  +  1  )  &amp;gt;  0 which is positive if and only if   (  x  &amp;gt;  3   and   x  &amp;gt;  −  1  )     or     (  x  &amp;lt;  3   and   x  &amp;lt;  −  1  ) i.e. if and only if   (  x  &amp;gt;  3  )     or     (  x  &amp;lt;  −  1  ).Step 3So the function is (strictly) increasing on the interval   (  −  ∞  ,  −  1  ] and on the interval   [  3  ,  ∞  ).The function is (strictly) decreasing on the interval   [  −  1  ,  3  ]

Determine the monotonic intervals of this function y=2x^3-6x^2-18x-7.

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