Questions
25S-STATS-102B-LEC-3 S25 Midterm Exam- Requires Respondus LockDown Browser
Multiple choice
Please select all the correct statements about the gradient.
Options
A.The gradient is always perpendicular to the tangent of the level curve.
B.The intercept of the hyperplane can be used to approximate the distance traveled by the algorithm.
C.The slope of the hyperplane is perpendicular to the gradient.
D.The gradient is always parallel to the tangent of the level curve.
E.The sign of the gradient indicates the direction of ascent or descent from a given point.
F.The slope of the hyperplane is parallel to the gradient.
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Step-by-Step Analysis
When evaluating statements about the gradient, we need to test each claim against standard multivariable calculus facts.
Option 1: 'The gradient is always perpendicular to the tangent of the level curve.' This is correct because the gradient at a point points in the direction normal to the level set (level curve in 2D, level surface in higher dimensions). The level curve is where the function has a constant value, so its tangent is orthogonal to the gradient.
Option 2: 'The intercept of t......Login to view full explanationLog in for full answers
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