Answer
Saddle point at $(\dfrac{6}{5},\dfrac{69}{25})$
Work Step by Step
Since, we have $f_x(x,y)=5y-14x+3=0, f_y(x,y)=5x-6=0$
After solving the above two equations, we get
$x=\dfrac{6}{5},y=\dfrac{69}{25}$
Thus the critical point is: $(\dfrac{6}{5},\dfrac{69}{25})$
As per second derivative test, we have
$D=f_{xx}f_{yy}-f^2_{xy}=-25$ and $D=-25 \lt 0$
Thus, saddle point at $(\dfrac{6}{5},\dfrac{69}{25})$
