Q. 124.7( 3 Votes )

For the curve y =

Answer :

The given curve y = 4x3 – 2x5


Then, the slope of the tangent at the point (x, y) is 12x2 – 10x4


The equation of the tangent at (x,y) is given by,


Y – y = (12x2 – 10x4)(X – x) ………….(1)


When the tangent passes through the origin (0,0), then X =Y=0


Then equation (1) becomes,


-y = (12x2 – 10x4)(– x)


y = (12x3 – 10x5)


Also, we have y = 4x3 – 2x5


(12x3 – 10x5) = 4x3 – 2x5


8x5 – 8x3 = 0


x5 – 2x3 = 0


x3(x2 – 1) = 0


x = 0 , 1


When x = 0 then y = 0


When x = 1 then y = 2


And when x = -1 then y = -2


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

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