MATH 2551-G MIDTERM 2
VERSION B
SUMMER 2025
COVERS SECTIONS 14.3-14.8, 15.1-15.4
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Show your work. Answers without work shown will receive little or no credit.
Question Points
1 2
2 2
3 2
4 4
5 4
6 10
7 6
8 10
9 10
Total: 50
, MATH 2551-G Midterm 2 Version B - Page 2 of 10 June 23, 2025
For problems 1-2 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) There does not exist a function f (x, y) which is continuous and has continuous
partial derivatives such that fx (x, y) = xey + 1 and fy (x, y) = x2 ey .
√
TRUE © FALSE
2. (2 points) Suppose f : R3 → R is differentiable at (a, b, c) with f (a, b, c) = d. Then the
linearization L(x, y, z) of f at the point (a, b, c) is also the equation of the plane tangent
to the level surface f (x, y, z) = d at the point (a, b, c).
√
© TRUE FALSE
3. (2 points) Select the statement below which is NOT true about gradients and directional
derivatives for a function f : R2 → R.
© A) If f is differentiable, −∇f (a, b) gives the direction of greatest decrease of f
at (a, b).
© B) If f is differentiable at (a, b), then the directional derivative exists in every
direction at (a, b).
√
C) If the directional derivative of f exists in every direction at (a, b),
then f is differentiable at (a, b)
© D) If f is differentiable, ∇f (a, b) is orthogonal to the level curve f (x, y) = f (a, b).
VERSION B
SUMMER 2025
COVERS SECTIONS 14.3-14.8, 15.1-15.4
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Show your work. Answers without work shown will receive little or no credit.
Question Points
1 2
2 2
3 2
4 4
5 4
6 10
7 6
8 10
9 10
Total: 50
, MATH 2551-G Midterm 2 Version B - Page 2 of 10 June 23, 2025
For problems 1-2 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) There does not exist a function f (x, y) which is continuous and has continuous
partial derivatives such that fx (x, y) = xey + 1 and fy (x, y) = x2 ey .
√
TRUE © FALSE
2. (2 points) Suppose f : R3 → R is differentiable at (a, b, c) with f (a, b, c) = d. Then the
linearization L(x, y, z) of f at the point (a, b, c) is also the equation of the plane tangent
to the level surface f (x, y, z) = d at the point (a, b, c).
√
© TRUE FALSE
3. (2 points) Select the statement below which is NOT true about gradients and directional
derivatives for a function f : R2 → R.
© A) If f is differentiable, −∇f (a, b) gives the direction of greatest decrease of f
at (a, b).
© B) If f is differentiable at (a, b), then the directional derivative exists in every
direction at (a, b).
√
C) If the directional derivative of f exists in every direction at (a, b),
then f is differentiable at (a, b)
© D) If f is differentiable, ∇f (a, b) is orthogonal to the level curve f (x, y) = f (a, b).
