MVT
For a CONTINUOUS function, the Mean Value Theorem states that there exists a point where the instantaneous rate of change is equal to this.
What is the average rate of change?
For a continuous function, the Extreme Value Theorem states there must be at least one minimum value and at least one of these.
What is a maximum value?
You can tell when a function is increasing because the derivative of the function will be this.
What is positive?
The First Derivative Test is used to determine if a function has this characteristic.
What is a maximum or minimum?
The Candidates Test not only checks critical points, but also these types of points.
What are endpoints?
For the function, f(x)=2x2+3, this is the value of f'(x) on the interval (0,1).
What is 2?
This type of point is located when the derivative is 0 or when the derivative does not exist.
What is a critical point?
If the rate of change of fruit flies is modeled by R(t)=2t(cos(t2)) where t is days, then at time t=3 the number of fruit flies is doing this.
What is decreasing?
When this changes from positive to negative, the function will have a maximum.
What is the derivative?
When using the Candidates Test, the lowest value produced is known as this type of point.
What is a global/absolute minimum?
This is where the derivative is equivalent to the average rate of change for the function y=ex on the interval (0, ln2). Round to the thousandths place.
What is 0.367?
This value is the critical point for the function f(x)=(ln x)2.
What is x=1?
For the function h(t)=500e-t, h(t) is decreasing at t=7 because of this reason.
What is h'(7)<0?
If given g'(x)=x2+5x+4, then there is a maximum on g(x) at this location.
What is x=-4?
Given f(x)=2x3+3x2+4 on the interval [-2,1], this x-value will give a global maximum of 9.
What is x=1?