In some situations, we would like to differentiate a function more than once. We call this higher-order differentiation, and we can define it in the following way: f(®(x) = f(x) flne1)(x) = (f\")'(x) . Caleulate f Chowyour working ii) Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For example, the polynomial above is of order 5, since it has highest non-zero coefficient c5 2. Show that f+1)(x)= 0 im) Now let )=si Caleulate iv) Fix some a e R. With f (x) = sin(x) as before, we define a new function g: N R such that g(n) = f(")(a). Write an alternative definition of g(n) that does not involve differentiation.
In some situations, we would like to differentiate a function more than once. We call this higher-order differentiation, and we can define it in the following way: f(®(x) = f(x) flne1)(x) = (f\")'(x) . Caleulate f Chowyour working ii) Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For example, the polynomial above is of order 5, since it has highest non-zero coefficient c5 2. Show that f+1)(x)= 0 im) Now let )=si Caleulate iv) Fix some a e R. With f (x) = sin(x) as before, we define a new function g: N R such that g(n) = f(")(a). Write an alternative definition of g(n) that does not involve differentiation.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 15CT
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