CALCULUS

Velocity, speed, acceleration

100

What is the rate at which velocity changes with time, in terms of both speed and direction.

Acceleration

200

When is an object decelerating?

When its velocity and acceleration have opposite signs

300

What does zero velocity indicate 

That an object is stationary and a possible change of direction may occur at time t

400

What is the derivative of a derivative function called

Second derivative

500

What is the mathematical link between: position&velocity/////velocity&acceleration

Derivative of the position is velocity

Derivative of velocity is acceleration

Extreme values

100

What are the extreme values on an interval of a function also called

Minimum/Maximum

200

Which type of function(s) has extreme maximum/minimum value(s)

EVEN DEGREE FUNCTIONS

300

What is the difference between local and absolute maximum/minimum

Absolute-Lowest/Highest point in the graph

Local-Lowest/Highest point in a given region

400

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

500

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.

Derivatives

100

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 (')

200

How do we find the derivative of a function

f'(x)=lim_x-->0f(x+h)-f(x)/h

300

How many ways can a derivative fail to exist

In three ways:

Cusp, Vertical Tangent, Discontinuity

400

Apply the power rule to f(x)=xⁿ in order to find its derivative

f'(x)=nx^n-1

500

Find the derivative of the following function:

f(x)=2x³+5x²+6x+7

f'(x)= 6x²+10x+6

Optimization

100

What is usually restricted when a function is optimized

The Domain

200

What is realizing the best possible outcome of a solution, subject to a set of restrictions

Optimizing it

300

True or False

The maximum or minimum can also occur at the ends of the restricted domain

True

400

When optimizing a function, what does the numerical value at the end represent

The extreme value of the model

500

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