Applications of Derivatives
Applications of Integrals
Differential Equations
Motion
Cryptic Calculus
200
The type of derivative used in a related rate problem.
What is a time derivative?
200
What is a volume of revolution?
200
A common method for solving a differential equation in which x and y are related through multiplication or division.
What is separation of variables?
200
|v(t)|
or
sqrt(x'(t)^2+y'(t)^2)
What is speed?
200
The silent pivot, where the curve ceases its current bend and veers toward a new direction.
What is a point of inflection?
400
Involves an objective subject to a constraint.
What is optimization?
400
The general name given to the value of
int_a^bf'(x)dx
What is net change?
400
(dP)/(dt)=kP(C-P)
What is a logistic differential equation?
400
If an object has v(t)<0 and a(t)>0 , then the object is this.
What is slowing down in the negative direction?
400
A curvature that beckons upwards, a cradle for growing change.
What is concave up?
600
L(x)approxf(x)
f''(x)<0
Then L(x) will do this to f(x) .
What is overestimate?
600
Evaluate the Pythagorean Theorem an infinite amount of times along a curve to get this.
What is arc length?
600
For Euler's method, it's the name given to the quantity (b-a)/n .
What is step size?
600
langlex''(t),y''(t)rangle
What is the acceleration vector?
600
A sequence of ever-approximating steps that inch toward an unreachable perfection, one term at a time.
What is a Taylor Series?
800
When a function’s slope flips signs around a critical point, this test confirms whether you’ve found a max or a min—or wasted your time.
What is the Second Derivative Test?
800
An approximation that balances the over- and underestimations of the area.
What is a Midpoint Riemann Sum?
800
The value needed to determine the correct solution curve on a slope field.
What is the initial value?
800
The type of equations best used to describe motion like this.
What are parametric equations?
800
A crossroads where slopes vanish or rise to a quiet peak, signaling a hidden shift.
What is a critical point?
1000
According to Rolle, a function f will have at least one point on an interval [a,b] with a horizontal tangent as long as this is true.
What is f(a)=f(b) ?
1000
(lim_(n to infty)sum_(i=0)^nf(x_i)Deltax)/(b-a)
What is average value?
1000
One of these contains an arbitrary constant, representing an entire family of functions, while the other satisfies a given initial condition.
What are a general solution and a particular solution?
1000
A particle moves along a line with velocity v(t) . The exact time at which the particle is farthest from its starting position can be found by identifying this type of critical point of the position function.
What is a local extrema of the position function?
1000
The quiet surrender of an infinite sequence, where disparate elements steadily draw together, inching ever closer to a single, elusive point of truth.
What is convergence?