Answer
$f(2)=3$.
Work Step by Step
The given equation is $f(x)=2x^3-5x^2+4x-1$.
If the given equation is divided by $x-2$ the remainder is $f(2)$.
Use synthetic division to divide.
Use synthetic division
$\begin{matrix}
2) &2&-5&4&-1 \\
& &4&-2&4 \\
& --&--&--& --\\
& 2&-1&2&3
\end{matrix}$
The remainder $3$, is the value of $f(2)$.
Check:
$\Rightarrow f(2)=2(2)^3-5(2)^2+4(2)-1$.
Simplify.
$\Rightarrow f(2)=16-20+8-1$.
$\Rightarrow f(2)=24-21$.
$\Rightarrow f(2)=3$.
