Show:
The Gradient Gatsby
2Chainz (Rule)
(Air)planes
One Direction(al Derivatives)
Awesomeness
100
The symbol for the gradient is called a...
What is a Nabla
100
g o f means
What is g compose f
100
What is the difference between the linear approximation formula and the tangent plane formula?
What is nothing
100
What is a directional derivative?
The rate of change at a point in a given direction
100
What does OASIS stand for?
Office of academic support and instructional services
200
True/False – The gradient at a given point gives the fastest rate of change.
True
200
f o c where f(x,y) = x^2-3xy and c(t) = at t=0
-3
200
Given this problem, how would you find the tan place to z = xy^2 -xy + 3yx^3 at (1,6). Explain the steps you would take.
Find the gradient, plug in the point, solve for z at (1,6) then plug into plane equation.
200
f(x,y) = x-y/(xy+2) in the direction of <12,5> at (1,-1)
21/13
200
What year were the Stonewall Riots?
1969
300
Calculate the nabla f(1,2,1) if f(x,y,z) = (x-y)z^3
(-1, 1, -3)
300
f o g where f(x,y,z) = cosx + siny + z^2 and c(t) = and t=π^(1/2)
π^(1/2)[-2+4π]
300
Find the tan place to z = xy^2 -xy + 3yx^3 at (1,6)
z = 48+ 84(x-1)+ 14(y-6)
300
At what direction does the function f(x,y,z) = x^2z +xyz + y^4z^3 increase/decrease the fastest at the point (1,1,1)?
What is <3,5,5>
300
What are the general steps for finding local extrema
Step 1 – Find critical points Step 2 – Second Derivative Test Step 3 – Classify the points
400
Find the gradient of f(x,y,z) = xcos(x^2), tan(y), e^(z^2+z^3)
Nabla f = cos(x^2) + 2x^2cos(x^2), sec^2(y), 6z^3e^(z^2+z^3)
400
I o u where I(x,y,z) = x+y+z and u(t) = when t= 3.
15+e^3
400
What is the equation of the plane tangent to f(x,y) = ye^(x^3+y^2)
z = e^2 + 3e^2(x-1) + 3e^2(y-1)
400
Find the direction where the directional derivative of f(x,y,z) cos(yz)3e^x at (0,0,0) is 2.
Any scalar multiple of <2,1,-2>
400
Find the extrema of f(x,y) = 5x-3y with the constraint of x^2 + y^2 = 136
(5/2,-3/2) max (-5/2, 3/2) min
500
A ball is moving along the path p(x,y,z) = zyx^3. At the point (1,1,1) what is the ball's fastest rate of decrease?
<-3,-1,-1>
500
Let z = ln(u^3 + v^4) where u = t^4 and v= t^2. Compute dz/dt
[12t^11 + 8t^7]/[t^12 + t^8]
500
(1.99^2 + 2.99^2)^(1/2)
13^(1/2) - 0.01(4/13^(1/2)) -0.01(27/13^(1/2))
500
Find the directional derivative of f(x,y) = yx^2 + lny at the point (1,1) in the direction towards (-1,-4)
-14/(29^(1/2))
500
Let f(x,y,z) = xyz be constrained by 1 = x + y + z. Assume x,y,z >=0. Find the global extrema.
Welcome Jacob to the board