Calculus Flashcards
What do slopes of >0, <0, and =0 indicate about the function?
> 0 - the slope is increasing
<0 - the slope is decreasing
=0 - the slope is flat
What is the derivative of X?
1
What is the derivative of a constant?
0
What is the trick to remember the quotient rule?
(Low * d-high) - (high * d-low) / square below
Two ways a square root can be expressed?
√x or x^1/2
What do you do to turn a negative power to positive?
x^-1 = 1/x
What does x0 or x naught represent?
x0 is a specific value of x or a specific point on the graph
What does f’(x0) > 0 represent?
That the function is increasing sloping at x = x0
What does f’(x0) < 0 represent?
That the function is decreasing sloping at x = x0
What is a critical point?
x0 is a critical point if the slope of the function at x0 is equal to zero ie f’(x0) = 0
What is a first order condition?
For a point x0 to be a max or min, a necessary condition is that x0 is a critical point. Not all critical points are a max/min but all max/min are critical points.
What do the first and second derivatives say about function?
The first derivative gives the function of the slope at a specific point and if it is increasing or decreasing. The second derivative tells if the function is concave or convex and if the point is a max or a min.
What does Young’s theorem require?
That the second derivative of two partial derivatives be the same.
Why use models?
Real world is complex and difficult to study, simplification of real world
What is the taxonomy for single variable optimization?
Max x - f(x)
