If f(x)=3 x^2+2 x f^{prime}(1)+f^{prime prime | vedclass

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(C) Given $f(x) = 3x^2 + 2x f'(1) + f''(2)$.Let $f'(1) = a$ and $f''(2) = b$.Then $f(x) = 3x^2 + 2ax + b$.Differentiating with respect to $x$,we get $

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$3 x^2-12 x+6$

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(C) Given $f(x) = 3x^2 + 2x f'(1) + f''(2)$.Let $f'(1) = a$ and $f''(2) = b$.Then $f(x) = 3x^2 + 2ax + b$.Differentiating with respect to $x$,we get $f'(x) = 6x + 2a$.At $x = 1$,$f'(1) = 6(1) + 2a = 6 + 2a$.Since $f'(1) = a$,we have $a = 6 + 2a$,which implies $a = -6$.Now,differentiating $f'(x) = 6x + 2a$ again,we get $f''(x) = 6$.Thus,$f''(2) = 6$.Since $f''(2) = b$,we have $b = 6$.Substituting $a = -6$ and $b = 6$ into the expression for $f(x)$:$f(x) = 3x^2 + 2(-6)x + 6 = 3x^2 - 12x + 6$.

If $f(x)=3 x^2+2 x f^{\prime}(1)+f^{\prime \prime}(2)$,then $f(x)=$ . . . . . .

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