Find the intervals in which the function f given by f ( x) = 2x ^3 - 3x ^2 - 36x + 7 is
  decreasing

Answers (1)

We have        f ( x) = 2x ^3 - 3x ^2 - 36x + 7

Differentiating the function with respect to x,  we get  :

                       f' ( x) = 6x ^2 - 6x - 36

or                                = 6\left ( x-3 \right )\left ( x+2 \right )

When          f'(x)\ =\ 0,   we have  :

                                              0\ = 6\left ( x-3 \right )\left ( x+2 \right )

or                                         \left ( x-3 \right )\left ( x+2 \right )\ =\ 0


So, three ranges are there   (-\infty,-2) , (-2,3) \ and \ (3,\infty)
Function    f^{'}(x)= 6x^{2} - 6x - 36  is positive in the interval  (-\infty,-2) , (3,\infty)   and negative in the interval  (-2,3)

So,               f(x) is decreasing  in  (-2, 3)

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