Question $4(1$ point$)$

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Which of the following statements are true?

$(1)$ If $D(a,b)>0$ and $f_{}(a,b)>0,$ then $f$ has a local minimum at $($a$,$b$).$

$(2)$ If then $f$ has a saddle point at $($a$,$b$)$

$(3)$ In implicit differentiation, $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}=\frac{F_y}{F_z}$

$(4)$ In implicit differentiation, $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}=-\frac{F_y}{F_z}$