Maximum/Minimum gradient of a curve

Find the minimum gradient of the curve y = 2x3 – 9x2 + 5x + 3 and the value of x when the minimum gradient occurs.

y = 2x3 – 9x2 + 5x + 3

gradient, m = 6x2 – 18x + 5
dm/dx = 12x – 18

minimum gradient,

dm/dx = 0

12x – 18 =0

X = 3/2 occurs at minimum gradient

= 6(3/2)2 – 18(3/2) + 5

= -17/2

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