Let
f(x)=3x5−2x4+7x3−5x2+4x−1. Answer the following:
a. (i) Find f′(x),f′′(x),f′′′(x),f(4)(x) and f(5)(x).
b. (ii) Show that f(5)(x) is a constant and state its value.
c. (iii) Verify that f(6)(x)=0 for all real x.
d. (iv) Evaluate f(5)(2). Comment on whether the result depends on the point chosen.