To determine the correct value of $a$ at a saddle point of the function, let's go over the steps involved in identifying a saddle point in a mathematical function.

Typically, a saddle point occurs when:

1. The first derivative with respect to $x$ and $y$ is zero at that point (which makes it a stationary point).
2. The second derivative test (Hessian matrix) indicates mixed concavity, i.e., the determinant of the Hessian matrix is negative at that point.

Without the function provided in "Question 14," we would typically:

• Set the partial derivatives of the function equal to zero to find values of $a$ that could give stationary points.
• Use the second derivative test to determine if any of these points is a saddle point (where the determinant of the Hessian is negative).

Given the options:

• If $a = 2$, $a = \frac{3}{2}$, $a = \frac{2}{3}$, and $a = 3$, we would calculate the Hessian determinant for each value to determine which one yields a saddle point.

If you can share the specific function or any further details from Question 14, I can help you solve for the exact value of $a$ that results in a saddle point.

Would you like more details on finding stationary points and saddle points in general, or do you have any other questions? Here are some related questions that might be helpful:

1. How do we calculate stationary points for functions with two variables?
2. What is the Hessian determinant, and how does it help identify saddle points?
3. What does it mean when the second derivative test fails?
4. Can there be multiple saddle points for a single function?
5. What are other methods to classify critical points besides the second derivative test?

Tip: When classifying critical points, always verify the sign of the Hessian determinant to distinguish between maxima, minima, and saddle points.