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Check that the functions f(t) =t and g(t) = e ^ t are linearly independent or not.
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- How is the linearization of f(x, y) centered at (a, b) defined?Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the directional derivative at the point (1, 4, 2).Find the gradient of the function w = xy2z2, and the maximum value of the directional derivative at the point (2, 1, 1).
- Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional derivative at the point (0, 1).How do I compute a value within 0.01 using linear approximation?