Punny Questions
Partial Derivatives
Gradients and Tangent Planes
Extrema
Second Order Partial Derivatives
100
The result of differentiating a cow
prime rib
100
the partial derivative with respect to X of (6xy + x4)
6y + 4x3
100
∇f(x, y), where
f(x, y) = 10x5y
<50x4y, 10x5>
100
True or false: the gradient of
f(x, y) = lny is 1/y
False
100
Find fxx(x,y) of the function
f(x,y)=2x^2y-3xy^2
f_(x x) (x,y)=4x-6
200
Why pirates good at calculus
A true pirate never forgets the C
200
the partial derivative with respect to x of
(2x3 + y2)1/2
3x2 / (2x3+y2)1/2
200
the directional derivative of f at the point (0, 1) in the direction 𝜃 = 𝜋/3 if
f(x, y) = y cos(xy)
sqrt(3)/2
200
The local max and min values and saddle points of the function f(x,y)=3xy - x2y - xy2
(Write max/min values as z-values and saddle points as ordered triples)
loc max of 1
saddle points at (0,0, 0), (0,3,0), and (3,0,0)
200
Find fxy of
f(x,y)=ln(xy)-cos(xy)
f_(x y) = xy cos(xy)
300
What you call a recycled calculus pun
derivative humor
300
Find fx, fy, and fz for
f(x, y, z) = x30y26z
f_(x) (x,y) = 30x^29y^26z
f_y (x,y)=26x^30y^26z
f_z (x,y) =x^30y^26
300
The equation of the plane tangent to
f(x,y) = ex cos y at the point (0,0,1)
z = x + 1
300
Find the critical points as an ordered triple (x,y,z) of
f(x, y) = 2x3 + 2y3 + 6xy
and label as a saddle point, local max, or local min.
Local Min at (1,1,-2)
Saddle Point at (0,0,0)
300
What does fxy describe about the graph of f?
It describes the twist of the surface.
400
Someone told me they didn't like calculus. So I told them...
That their opinion changes over time.
400
Is fx positive, negative, or zero at the point (0,-1)
f_x(0,-1) = 0
400
The maximum rate of change of f at the point (4, 1) AND the direction vector in which it occurs if
f(x,y)=4ysqrtx
max rate of change =
sqrt(65)
direction vector =
(1/sqrt(65))<1, 8>
400
Find the critical points of
f(x,y) = x^2y+2y^2-2xy+6
(1,1/4), (0,0), (2,0)
400
A tin can is supposed to have a radius of 1.5 inches and a height of 4 inches. Use differentials to estimate the propagated error in the surface area of the can if the radius has a max error of 0.2 inches and the height has a max error of 0.3 inches.
3.7 square inches
500
What kind of aircraft do calculus teachers fly?
They fly tangent planes.
500
the partial derivative with respect to x of (2yx4e(2xy+1))
8yx3e2xy+1 + 4y2x4e2xy+1
500
Let f be a function of two variables that has continuous partial derivatives and consider the points A(7, 1), B(8, 1), C(7, 11), and D(16, 13). The directional derivative of f at A in the direction of the vector AB is 4 and the directional derivative at A in the direction of AC is 2. Find the directional derivative of f at A in the direction of the vector AD.
4
500
Find the critical points and label as saddle point, local max, or local min of the function
f(x,y) = x^3+y^2-3x^2+10y+6
Saddle point (0,-5)
Local minimum (2,-5)
500
For the contour diagram of f(x,y) below, determine if fx, fy, fxx, and fyy are positive, negative, or zero at point P. 
fx > 0, fxx < 0
fy < 0, fyy > 0