Show:
Differential Equations
Miscellaneous Differentiation
Differentiation Facts
Name the Derivative Rule
Rates of change
100
When solving a differential equation, you should first _____ then _____.
What is separate & integrate
100
If f is strictly monotonic on its entire domain, then its one-to-one and therefore has an ______ function.
What is inverse
100
Since the definition of a derivative is a limit, the derivatives must approach the same value from the _____ and _____ in order to be differentiable.
What is left & right
100
d/dx [x^n]
What is the power rule
100
this rate of change is depicted as distance/change in time
What is average rate of change or "AROC"
200
The two types of solutions you can find when solving differential equations are _____ and _____.
What is general & particular
200
Find the derivative of the function h(x)=ln(2x^2+1)
What is h'(x)=4x/(2x^2+1)
200
True or False: If a function is continuous, it is differentiable.
What is false
200
d/dx[cf(x)]
What is the constant multiple rule
200
This type of velocity is written as lim as deltat approaches 0 of s(t+delta t)-s(t)/(delta t)=f'(t)
What is instantaneous velocity "IROC"
300
If you are given dy/dx=1/(2x-1) (4,2) to solve you must separate, integrate, then plug in the _____ _____ and solve for _.
What is initial conditions & c
300
This kind of differentiation attaches a dy/dx to the derivative of each y
What is implicit differentiation
300
True or false: If a function is differentiable, it is continuous.
What is true
300
d/dx[f(x)/g(x)]
What is the quotient rule
300
Average rate of change is a _____ between two points.
What is a slope
400
Find the general solution of the following differential equation: dy/dx = (1/2)x-1
What is (1/4)x^2 - x + C
400
This kind of line requires you to plug x, y, and the derivative (slope) to the equation
What is a tangent line
400
How is the definition of a derivative written?
What is the limit as x approaches 0 of f(x+deltax)-f(x)/(deltax)
400
d/dx[f(g(x))]
What is the chain rule
400
Find the average rate of change of f(x)=x-2 over the interval (1,3)
What is [f(3)-f(1)]/(3-1)=1
500
Find the general solution of the following differential equation: dy/dx=2y
What is y=+/- ce^(2x)
500
This kind of theorem gives conditions that guarantee the existence of an extreme value in the interior of a closed interval.
What is Extreme Value Theorem
500
How is the alternate form of a derivative written? (used for a derivative of a point)
What is f'(c)=limit as x approaches c of f(x)-f(c)/(x-c)
500
d/dx [c] =?
What is constant rule
500
What is the name of the function:s(t)=1/2g(t)^2+v(initial velocity)t+s(initial position)t
What is the position function.