Find the intervals in which the function `f(x)=2x^3+9x^2+12 x+20` is increasing and decreasing.

Explanation

Let `f(x)=2x^3−9x^2+12x+20`

`f′(x)=6x^2−18x+12`

=`6(x^2−3x+2)=6(x−1)(x−2)`

`f′(x)=0` gives us

`6(x−1)(x−2)=0⇒x=1,2`

The points x=1,2 divide the real lline into three intervals `(−∞,1),(1,2),(2,∞)`

1)In the interval`(−∞,1)`

`f′(x)>0`∴f(x) is increasing in `(−∞,1)`


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