The polynomial functions that has the largest second derivative at x = 0 is; y = x³ + 2x² - 5x + 10
<h3>How to find the second derivative of a Polynomial?</h3>
The second derivative of a function is simply defined as the derivative of the function's derivative.
Thus;
A) If y = 5x⁵ - x³ + 4x
dy/dx = 25x⁴ - 3x² + 4
d²y/dx² = 100x³ - 6x
Thus at x = 0, we have;
d²y/dx² = 0
B) y = 3x⁴ + x² + 16
dy/dx = 12x³ + 2x
d²y/dx² = 36x² + 2
At x = 0, the second derivative is;
d²y/dx² = 2
C) y = 4x⁶ + x² - 1
dy/dx = 24x⁵ + 2x - 1
d²y/dx² = 48x⁴ + 2
At x = 0, the second derivative is;
d²y/dx² = 2
D) y = x³ + 2x² - 5x + 10
dy/dx = 3x² + 4x - 5
d²y/dx² = 6x + 4
At x = 0, the second derivative is;
d²y/dx² = 4
E) y = 10x⁵ + 3x³ - 7x + 2
dy/dx = 50x⁴ + 9x² - 7
d²y/dx² = 200x³ + 18x
At x = 0, the second derivative is;
d²y/dx² = 0
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