Show there is a unique cubic polynomial p(x)for which p(x_0 )=f(x_0 ) p(x_2 )=f(x_2 );p^' (x_1 )=f(x_1 ); p"(x_1)=f(x_1) where f(x) is a given...

Show there is a unique cubic polynomial p(x)for which p(x_0 )=f(x_0 )p(x_2 )=f(x_2 );p^' (x_1 )=f(x_1 ); p"(x_1)=f(x_1) where f(x) is a given function and x_0≠x_2.Derive a formula for p(x),analogous to the Lagrnage formulafor ordinary interpolation.