Determine whether each statement is true of false. a. If the parametric curve x

Question

Determine whether each statement is true of false. a. If the parametric curve x = f(t), y = g(t) satisfies g'(1) = 0, then it has a horizontal tangent when t = 1. True False If u rightarrow middot v rightarrow = 0, nad u rightarrow x v rightarrow = 0 rightarrow, then u rightarrow = 0 or v rightarrow = 0 True False If f has continuous partial derivatives of all order on R^3 and C is an open region, then integral_C delta f middot dr rightarrow = 0 True False If f(x, y) has tow local maxima, then f must have a local minimum True False There exists a function f with continuous second-order partial derivatives such that f_x (x, y) = x +y^2 and f_y (x, y) = x - y^2. True False

Explanation / Answer

Solution:

a. False

b. Fase

c. True

d. True

e. False

e.

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