Evaluate the Function f(2)=3x^4+x^3-2x^2+x+12

$f (2) = 3 x^{4} + x^{3} - 2 x^{2} + x + 12$

Replace the variable $x$ with $2$ in the expression.

$f (2) = 3 {(2)}^{4} + {(2)}^{3} - 2 {(2)}^{2} + 2 + 12$

Simplify the result.

Remove parentheses.

$f (2) = 3 {(2)}^{4} + {(2)}^{3} - 2 {(2)}^{2} + 2 + 12$

Simplify each term.

Raise $2$ to the power of $4$ .

$f (2) = 3 \cdot 16 + {(2)}^{3} - 2 {(2)}^{2} + 2 + 12$

Multiply $3$ by $16$ .

$f (2) = 48 + {(2)}^{3} - 2 {(2)}^{2} + 2 + 12$

Raise $2$ to the power of $3$ .

$f (2) = 48 + 8 - 2 {(2)}^{2} + 2 + 12$

Raise $2$ to the power of $2$ .

$f (2) = 48 + 8 - 2 \cdot 4 + 2 + 12$

Multiply $- 2$ by $4$ .

$f (2) = 48 + 8 - 8 + 2 + 12$

Simplify by adding and subtracting.

Add $48$ and $8$ .

$f (2) = 56 - 8 + 2 + 12$

Subtract $8$ from $56$ .

$f (2) = 48 + 2 + 12$

Add $48$ and $2$ .

$f (2) = 50 + 12$

Add $50$ and $12$ .

$f (2) = 62$

The final answer is $62$ .

$62$