The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.
Step 1: Differentiate y with respect to x. dy/dx = 3x^2 - 6x - 9
Step 2: Equate to zero and solve. 3x^2 - 6x - 9 = 0(x - 3)(x+1) = 0x = 3, x = -1
Step 3: Substitute into original equation to find y. At x = 3, y = -13. ==>> (3, -13)At x = -1, y = 19 ==>> (-1, 19)
Step 4: Find the second derivatived^2y/dx^2 = 6x - 6
Step 5: Determine the nature of the stationery pointsAt x = 3, d^2y/dx^2 = 12Therefore, (3, -13) = MINIMUMAt x = -1, d^2y/dx^2 = -12Therefore, (-1, 19) = MAXIMUM
DA
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