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(C) Given $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$.Let $f'(1) = a$,$f''(2) = b$,and $f'''(3) = c$.Then $f(x) = x^3 + ax^2 + bx + c$.Now,find the

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$-2$

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(C) Given $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$.Let $f'(1) = a$,$f''(2) = b$,and $f'''(3) = c$.Then $f(x) = x^3 + ax^2 + bx + c$.Now,find the derivatives:$f'(x) = 3x^2 + 2ax + b$$f''(x) = 6x + 2a$$f'''(x) = 6$Using the definitions of $a, b, c$:$c = f'''(3) = 6$.$b = f''(2) = 6(2) + 2a = 12 + 2a \Rightarrow 2a - b = -12$.$a = f'(1) = 3(1)^2 + 2a(1) + b = 3 + 2a + b \Rightarrow a + b = -3$.Adding the two equations: $(2a - b) + (a + b) = -12 - 3 \Rightarrow 3a = -15 \Rightarrow a = -5$.Substituting $a = -5$ into $a + b = -3$: $-5 + b = -3 \Rightarrow b = 2$.Thus,$f(x) = x^3 - 5x^2 + 2x + 6$.Calculating $f(2)$: $f(2) = (2)^3 - 5(2)^2 + 2(2) + 6 = 8 - 20 + 4 + 6 = -2$.

Let $f: R \to R$ be a function such that $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$,for all $x \in R$. Then $f(2)$ is equal to

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