If the tangent at a point P on the curve y=4x^4+x is perpendicular to the tangent to the same curve at (0 ,0 ), then the point P is

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Accepted Answer

Correct answer: A. (a) Given equation of curve, y=4x^4+x Tangent at P is dy dx=16x^3+1 According to question. It is perpendicular to tangent at (0 ,0 ). Slope of tangent at (0 ,0 )m_2= ( dy dx )_ (0 ,0 )=1 According to question, Hence 16x^3+1=-1 x^3= -1 or x= -12 Putting it in equation of curve ∴y=4 ( -12 )^4+ ( -12 )= -14y=(- 12)^4+(- 12)= -14 ∴P ( -12 , -14 )

$If the tangent at a point P on the curve y = 4 x^{4} + x is perpendicular to the tangent to the same curve at (0, 0), then the point P is$

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