NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The abscissa(e) of the point(s), where the tangent to curve y = x 3 - 3 x 2 - 9 x + 5 is parallel to the x -axis is(are)

Options

Ax = 0
Bx = 1 and - 1
Cx = 1 and - 3
Dx = - 1 and 3

Correct answer

D. x = - 1 and 3

Step-by-step solution

y = x 3 - 3 x 2 - 9 x + 5 ⇒ d y d x = 3 x 2 - 6 x - 9 We know that this equation gives the slope of the tangent to the curve. The tangent is parallel to x -axis. Therefore, 3 x 2 - 6 x - 9 = 0 ⇒   x = - 1 ,   3 .

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