JEE Main202126 Feb 2021Morning ShiftMathematicsApplication of DerivativesActual

The maximum slope of the curve y = 1 2 x 4 - 5 x 3 + 18 x 2 - 19 x occurs at the point

Options

A3 , 21 2
B2 , 2
C2 , 9
D0 , 0

Correct answer

B. 2 , 2

Step-by-step solution

d y d x = 2 x 3 - 15 x 2 + 36 x - 19 Since, slope is maximum so, d 2 y d x 2 = 6 x 2 - 30 x + 36 = 0 ⇒ x 2 - 5 x + 6 = 0 x = 2 , 3 at x = 2 d 3 y d x 3 = 12 x - 30 at x = 2 , d 3 y d x 3 < 0 So, maxima y = 1 2 × 16 - 5 × 8 + 18 × 4 - 19 × 2 = 8 - 40 + 72 - 38 = 80 - 78 = 2 point 2 , 2

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