NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The slope of the tangent to the curve y = x 3 + x + 54 which also passes through the origin is

Correct answer

Step-by-step solution

Let point P x 1 , y 1 be the point on this curve such that the tangent of P passes through the origin. Equation of tangent at P is y - y 1 = 3 x 1 2 + 1 x - x 1 It passes through 0 , 0 so y 1 = 3 x 1 2 + 1 x 1 ⇒ x 1 3 + x 1 + 54 = 3 x 1 3 + x 1 ⇒ x 1 3 = 27 ⇒ x 1 = 3 So, d y d x x 1 , y 1 = 3 x 1 2 + 1 = 3 9 + 1 = 28

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