Answer :
Invent an nth degree poly and then check whether this statement is true or false.
Suppose we let F(x)=x^3. This is a 3rd degree poly. F^(n+1)(x) would be F^(3+1)(x), or F^4(x), or (x^3)^4, or x^12. If this last expression were 0, that would be coincidential. Thus, I'd answer FALSE.
Suppose we let F(x)=x^3. This is a 3rd degree poly. F^(n+1)(x) would be F^(3+1)(x), or F^4(x), or (x^3)^4, or x^12. If this last expression were 0, that would be coincidential. Thus, I'd answer FALSE.
The given proposition is true as the number of Derivatives of a Polynomial function is bounded by its Grade.
In Differential Calculus, if function is a Polynomial, then its number of Derivatives is bounded by its Grade, which is the maximum integer Exponent of the Polynomial. Then, there [tex]n[/tex]-th degree Polynomial has only [tex]n+1[/tex] derivatives, where [tex]\frac{d^{n+1}f}{dx^{n+1}} = 0[/tex].
Therefore, the given proposition is true as the number of Derivatives of a Polynomial function is bounded by its Grade.
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