WILL MEDAL AND FOLLOW! Calc Question.

A function f, which has derivatives for all orders for all real numbers, has a 3rd degree Taylor polynomial for f centered at x = 4.

The 4th derivative of f satisfies the inequality the 4th derivative of x is less than or equal to 5 for all x the interval from 3.5 to 4 inclusive. Find the LaGrange error bound if the 3rd degree Taylor polynomial is used to estimate f (3.5).

Question

WILL MEDAL AND FOLLOW! Calc Question.

A function f, which has derivatives for all orders for all real numbers, has a 3rd degree Taylor polynomial for f centered at x = 4.

The 4th derivative of f satisfies the inequality the 4th derivative of x is less than or equal to 5 for all x the interval from 3.5 to 4 inclusive. Find the LaGrange error bound if the 3rd degree Taylor polynomial is used to estimate f (3.5).

anonymous · Answer

The inequality is $$f^4(x)\le5$$