Practice: Gradient & Tangent

9 multiple choice · 4 free response · 1 walkthroughs

Q1.

intermediateFinal Review #61

f (x, y) = x^{2} e^{y z}

— wait,

f

should depend on three variables. Let

f (x, y, z) = x^{2} e^{y z}

. The gradient is

Q2.

basic

The direction in which

f (x, y, z) = x^{2} + 2 y^{2} + 3 z^{2}

increases most rapidly at

(1, 1, 1)

Q3.

basic

D_{u} f

is **maximized** when

u

Q4.

intermediate

Tangent plane to

z = x^{2} + y^{2}

(1, 1, 2)

has equation

Q5.

intermediate

The gradient is **always**

Q6.

basicFinal Review #56

Use linearization to estimate

f (2.1, 4.95)

f (2, 5) = 6, f_{x} (2, 5) = 3, f_{y} (2, 5) = - 1

Q7.

intermediate

D_{\overset{v}{^}} f (P) = 0

for unit vector

\overset{v}{^}

, then

Q8.

basic

Maximum value of the directional derivative of

f

P

Q9.

basic

True/False: At every point on a smooth surface

z = f (x, y)

, there is a unique tangent plane.