Consider the polynomial .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the polynomial f(x)=x6−3x4+2x2−8f(x)=x^6-3x^4+2x^2-8. (i) Find the first derivative f′(x)f'(x). (ii) Find the second derivative f′′(x)f''(x). (iii) Determine the fourth derivative f(4)(x)f^{(4)}(x). (iv) For what smallest non-negative integer kk is f(k)(x)f^{(k)}(x) identically zero for all real xx? Write down that derivative.

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