Velocity, speed, acceleration
What is the rate at which velocity changes with time, in terms of both speed and direction.
Acceleration
What are the extreme values on an interval of a function also called
What are derivatives and what are they donated by
The rate of change of a function with respect to a variable
They are donated by a prime sign (')
What is usually restricted when a function is optimized
When is an object decelerating?
When its velocity and acceleration have opposite signs
Which type of function(s) has extreme maximum/minimum value(s)
EVEN DEGREE FUNCTIONS
How do we find the derivative of a function
f'(x)=limx-->0f(x+h)-f(x)/h
What is realizing the best possible outcome of a solution, subject to a set of restrictions
Optimizing it
What does zero velocity indicate
That an object is stationary and a possible change of direction may occur at time t
Absolute-Lowest/Highest point in the graph
Local-Lowest/Highest point in a given region
In three ways:
Cusp, Vertical Tangent, Discontinuity
True or False
The maximum or minimum can also occur at the ends of the restricted domain
True
What is the derivative of a derivative function called
Second derivative
True or False
A function that is discontinuous on a closed interval has both an absolute maximum value and an absolute minimum value on that interval
False
Apply the power rule to f(x)=xn in order to find its derivative
f'(x)=nxn-1
When optimizing a function, what does the numerical value at the end represent
The extreme value of the model
What is the mathematical link between: position&velocity/////velocity&acceleration
Derivative of the position is velocity
Derivative of velocity is acceleration
How to find extreme values of a function
set f'(x)=0 and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.
Find the derivative of the following function:
f(x)=2x3+5x2+6x+7
f'(x)= 6x2+10x+6
List the Algorithm steps for solving optimization problems
1. Determine a function in one variable that represents the function to be optimized
2. Whenever possible, draw a diagram, labelling the given and required quantities
3. Determine the domain of the function to be optimized
4. Determine the derivative and zeros of derivative
5. Solve f'(x) for when x=the zeros and the domain