Suppose f(x) = $x ^ { 4 }$ - 7 $x ^ { 3 }$ + 2. The third Taylor polynomial of f(x) at x = 1 is $\mathrm { P } 3 ( x ) = 2 - 7 x ^ { 3 }$ .

Question

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The third Taylor polynomial, $P_3(x)$, for a function $f(x)$ at $x = a$ includes terms up to the third derivative of $f(x)$ evaluated at $x = a$, and the given polynomial $P_3(x) = 2 - 7x^3$ does not correctly represent the third Taylor polynomial of $f(x) = x^4 - 7x^3 + 2$ at $x = 1$, as it should include terms derived from $f(x)$, $f'(x)$, $f''(x)$, and $f'''(x)$ evaluated at $x = 1$, and properly scaled by factorial terms.

Suppose F(x) = x4x ^ { 4 }x4 - 7 x3x ^ { 3 }x3

Suppose F(x) = $x ^ { 4 }$ - 7 $x ^ { 3 }$