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The quadratic approximation of f(x) = x³ - 3x² - 5 at the point x = 0 is

1. 3x² - 6x - 5
2. -3x² - 5
3. -3x² + 6x - 5
4. 3x² - 5

Correct answer: -3x² - 5

Solution

The quadratic approximation at a point is derived from the function's value and its first two derivatives at that point. For f(x) = x³ - 3x² - 5 at x = 0, the function value is -5 and the second derivative is -6, leading to the approximation -3x² - 5.

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