Question 39: The graph of the function y = x3 – 3×2 – 9x – 5 has a minimum point of

We have: D = R and y’ = 3x^{2} – 6x – 9, y’’ = 6x – 6.

Hence y’ = 0 ⇔ x = -1 ∨ x = 3.

Since y”(-1) = -12 < 0 and y''(3) = 12 > 0, the function has a minimum at x = 3.

Graph of the function y = x^{3} – 3x^{2} – 9x – 5 has a minimum score of (3; 32).

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