Find the third order polynomial

Question

Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=-3, f''(0)=8, and f'''(0)=24. Write the third order polynomial for f at x=0 and use it to approximate f(0.4).

Answer 1

a third order poly has a constant third derivative. plug in 24 and integrate. repeat.