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

Explanation

Slope of x - axis is 0

`Let (x_{1}, y_{1})` be the required point.


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


Since `(x_{1}, y_{1})` lies on the curve . Therefore


`y_{1}=2 x_{1}{ }^{3}-15 x_{1}^{2}+36 x_{1}-21 ldots text { (1) }`

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