ENGR 251 Midterm: ENGR 251 Midterm 2015 Winter Solutions
Document Summary
Emat 233 - solutions to second midterm exam - winter 2005. Answer: first we nd the gradient ~ f = f logarithm and the chain rule, we compute: 1 x2 + y2 (2x) = x x2 + y2 . To nd the directional derivative in the direction of 2i + 3j, we must use a unit vector in that direction: u = Duf (1, 1) = ~ f (1, 1) u = Find the maximum value of the directional derivative at this point. The maximum value of the directional derivative is then equal to k~ fk. In this case, at the point (1, 1) the function increases most rapidly in the direction of ~ f (1, 1) = 1. 2 j, with a maximum rate of increase of. = s1 k~ f (1, 1)k = s(cid:16) 1. 2 (note that the direction of ~ f is the direction pointing radially outward from the origin.
