Solutions to Math 230 Test 2Winter Quarter 2014Page 2 of 10Question 1(12 points, 2 points each).True or False? Circle the correct answer.(a) If a functionf(x, y)is differentiable at(a, b), then the function is continuous at(a, b).
(b) If a particle moves at constant speed, then the acceleration is zero.
(c) If all directional derivatives of a functionf(x, y)at(0,0)are the same, then thegradient vector at(0,0)is zero.
(d) The directional derivative of a functionf(x, y)in the direction ofh1,1iisfx(x, y)+fy(x, y).
(e) Two curves which are tangent to each other at a point (i.e., share a commontangent line) must have the same curvature at that point.
(f) Ifu(t)andv(t)are vector-valued functions, then(u(t)×v(t))0=u0(t)×v0(t).