Question

Use

Taylor series to drive the backward difference formula to estimate
the second derivative
Q(4) a) Use Taylor series to drive the backward difference formula to estimate the second derivative \( (f(x)) \). b) Using the table in \( Q(3) \), approximate \( \dot{f}(19) \) using forward, backwa

Answer 1

To estimate the second derivative using a backward difference formula, we can use Taylor series to derive the formula. The formula for the second derivative is (f(x) - 2f(x-h) + f(x-2h)) / h^2, where h is the step size. This formula provides an approximation of the second derivative at a specific point.

Step-by-step explanation:

To estimate the second derivative using a backward difference formula, we can use Taylor series. The formula for the second derivative is:

f''(x) = (f(x) - 2f(x-h) + f(x-2h)) / h^2

where h is the step size. This backward difference formula provides an approximation of the second derivative of a function at a given point.