Final answer:
Partial derivatives can be estimated from contour maps using the Central Difference Method, which utilizes the orientation and spacing between contour lines to estimate the gradient at a point. The correct answer is option (D)
Step-by-step explanation:
Partial derivatives of a function can be estimated from contour maps by analyzing the spacing and orientation of the contour lines. A contour map illustrates lines of constant function values, known as level curves or contour lines. These lines allow us to visually estimate the gradient of a function at a particular point.
To determine the gradient direction, you should look for the direction that is perpendicular to the contour line at that point. This is because the gradient of a function points in the direction of the steepest ascent. Moreover, the spacing between contour lines indicates the magnitude of the gradient; closely spaced lines suggest a steep gradient, while widely spaced lines indicate a gentle slope. Therefore, an answer regarding estimating partial derivatives from contour maps would be the Central Difference Method (Option D), which uses points surrounding our target point to estimate the gradient at that point.
The other options are not directly related to estimating partial derivatives from contour maps: Gradient Descent (A) is an optimization algorithm, the Jacobian Matrix (B) represents derivatives of vector-valued functions, and Contour Integration (C) is a method of evaluating integrals along curves in the complex plane.