The directional derivative 3'30}, (3) is parallel to 11. TRUE FALSE 2. If f(m, g) has a local maximum at (a, b) subject to the constraint g(:r,y) =...

Calculus: True and false questions on contours, directional derivative, and local max/min.

1. The directional derivative 3’30}, (3) is parallel to 11. TRUE FALSE 2. If f(m, g) has a local maximum at (a, b) subject to the constraint g(:r,y) = c, then g(a,b) = c. TRUE FALSE 3. If f(:c, g) has a local maximum at (a, b) subject to the constraint 9(m, y) = c, then gradf(o, b) = TRUE FALSE 4. The function f(.1:, y) = a: + y has no global maximum subject to the constraint .1: - y = 0. TRUE FALSE 5. The contours of f(r£,y) = m2 — y2 cross the contours of g(.1:, y) = my at right angles. (Hint:Think about the geometric properties of the gradient vector.) TRUE FALSE