At what point will be tangents to the curve `y=2x^3-15 x^2+36 x-21` by parallel to x=axis? Also, find the equations of the tangents to the curve at these points.

Explanation

`y=2 x^{3}-15 x^{2}+36 x-21`

`frac{d y}{d x}=6 x^{2}-30 x+36`

`text { Now, }frac{d y}{d x}=0`

`text { or, } 6 x^{2}-30 x+36=0`

`text { or, } x^{2}-5 x+6=0`

`text { or, } x^{2}-3 x-2 x+6=0`

`text { or, } x(x-3)-2(x-3)=0`

`x=2, x=3`

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