For the curve y = 4x^ 3 – 2x ^5 , find all the points at which the tangent passes through the origin.

Given: Equation of the curve  ……….(i)

  Slope of the tangent at  passing through origin (0, 0)

= 

= 

  

 

Substituting this value of  in eq. (i), we get,

 

 

  or 

  or 

 From eq. (i), at 

From eq. (i), at 

From eq. (i), at 

Therefore, the required points are (0, 0), (1, 2) and