MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
Let
f(x)=3x5−2x4+7x3−5x2+4x−1. Answer the following:
(i) Find f′(x),f′′(x),f′′′(x),f(4)(x) and f(5)(x).
(ii) Show that f(5)(x) is a constant and state its value.
(iii) Verify that f(6)(x)=0 for all real x.
(iv) Evaluate f(5)(2). Comment on whether the result depends on the point chosen.