Let y = x 3 - 6 x 2 + 9 x + 1 be the equation of a curve, then the x -intercept of the tangent to this curve whose slope is least, is

Question

Let y = x 3 - 6 x 2 + 9 x + 1 be the equation of a curve, then the x -intercept of the tangent to this curve whose slope is least, is,

MARKS App · Accepted Answer

d y d x = 3 x 2 - 4 x + 3 = 3 x - 2 2 - 1 ≥ - 3 So, minimum value is - 3 when x = 2 at x = 2 , y = 3 Hence, equation of tangent is 3 x + y = 9 So, x -intercept = 3

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