Particle Motion
This is the derivative of position with respect to time.
What is Velocity?
The IVT applies only to functions that have this property on an interval.
What is continuity?
The EVT guarantees a function has both a maximum and minimum if it is continuous on this type of interval.
What is a closed interval?
The MVT requires continuity on [a, b] and this on (a, b).
What is differentiability?
Linearization uses this line to approximate a function near a point.
What is the tangent line?
If velocity is positive, the particle is moving in this direction along a number line.
What is to the right (/positive)?
If a function is continuous on [a, b], it takes every value between f(a) and this.
What is f(b)?
The two types of extreme values are absolute maximum and this.
What is absolute minimum?
The MVT guarantees a point where the tangent slope equals this slope.
What is the average rate of change?
In y − f(a) = f′(a)(x − a), this represents the slope of the line.
What is f′(a)?
When velocity is increasing, this must be true about acceleration.
What is acceleration is positive?
The IVT guarantees at least one solution to f(x) = k if k is between these two values.
What are f(a) and f(b)?
To find extrema on a closed interval, you check critical points and these two points.
What are the endpoints?
The average rate of change is calculated using this formula.
What is (f(b) − f(a)) / (b − a)?
Linearization is most accurate when x is this relative to a.
What is close to a?
A particle changes direction when velocity does this.
What is changes sign?
The IVT guarantees existence of a solution, but not this.
What is uniqueness (only one solution)?
A critical point occurs where the derivative is zero or this.
What is undefined?
The MVT guarantees at least one value c in this interval.
What is (a, b)?
If f(2) = 5 and f′(2) = 3, the linearization equation is this.
What is y − 5 = 3(x − 2)?
A particle is slowing down when velocity and acceleration have this relationship.
What is opposite signs?
If f(1) = -2 and f(3) = 5 and f is continuous, the IVT guarantees a root exists in this interval.
What is (1, 3)?
A function that is continuous on (a, b) but not [a, b] may fail to have this guaranteed by EVT.
What is an absolute max or min?
If f′(x) = 0 for all x in (a, b), the function must be this.
What is constant?
In y−f(a)=f′(a)(x−a), what do f(a) and f′(a) represent?
What is: f(a), the function value, and f′(a), the slope of the tangent line?