The contour plot represents a scalar field where each contour line represents a constant value. The steepest ascent in such a plot corresponds to the direction of the gradient, which always points perpendicular to the contour lines and toward increasing values.

From the plot:

• Arrow (1) points directly toward the center (where the values are lower), indicating descent.
• Arrow (2) points perpendicular to the contours but outward toward increasing values.
• Arrow (3) points away from the center but slightly at an angle that isn't perfectly perpendicular to the contours.
• Arrow (4) points outward but also along the contour lines, not perpendicular.

The direction of steepest ascent is always perpendicular to the contour lines and points toward increasing values. Thus, Arrow (2) points in the direction of the steepest ascent.

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Related Questions:

1. What is the mathematical definition of the gradient in multivariable calculus?
2. How do contour plots represent scalar fields and gradients?
3. Why does the gradient always point perpendicular to contour lines?
4. How do you calculate the magnitude of the steepest ascent from a contour plot?
5. Can gradient directions change depending on the field?

Tip:

The gradient vector always points in the direction of maximum rate of increase of the function at any given point.