Consider the polynomial f(x)=x6−3x4+2x2−8.
a. (i) Find the first derivative f′(x).
b. (ii) Find the second derivative f′′(x).
c. (iii) Determine the fourth derivative f(4)(x).
d. (iv) For what smallest non-negative integer k is f(k)(x) identically zero for all real x? Write down that derivative.