Question

Which of these polynomial functions has the largest second derivative at X=0?

Answer 1

The polynomial functions that has the largest second derivative at x = 0 is; y = x³ + 2x² - 5x + 10

How to find the second derivative of a Polynomial?

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

Read more about Second derivative at; brainly.com/question/2154132

#SPJ1