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

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

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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).

Posted by

Devendra Khairwa

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