Limits
Derivatives
Derivative Applications
Vocab...
...ulary
100
True/False: If f(a) is undefined, then the limit as x approaches a will also be undefined.
What is false? (Not necessarily true - removable discontinuity).
100
Given g(x)=7x^3+9x^2+5x, this is g'(-1).
What is 8?
100
If f'(a)=0 and f''(a)<0, then x=a must be the location of this.
What is a relative maximum?
100
The following are two conditions for continuity: A. f(a) is defined. B. the limit as x approaches a for f(x) exists. This is the third condition.
What is the limit as x approaches a of f(x) equals f(a)?
100

Name 2 of the 4 ways a function can fail to be differentiable.

What are: a) cusp, b) corner, c) discontinuity, d) vertical tangent.

200

These are two ways you can evaluate a limit in indeterminate form.

What are factoring, rationalizing the denominator, or l'hopital's rule?

200
This is the derivative of f(x)=(4-2x)(x^2+1)^3
What is f'(x)=-2(x^2+1)^2(7x^2-12x+1)
200
If f is the function defined by f(x)=3x^5-5x^4, what are the intervals on which f(x) is concave up?
What is (1, infinity)?
200
This is what the second derivative indicates about a function.
What is concavity?
200
These are the two ways to determine where a critical point of a function occurs.
What is where the number makes the derivative equal to zero or undefined?
300

Do this to determine the horizontal asymptotes of a function?

What is finding the limit as x approaches infinity)?

300
This is the derivative of f(x)=3/2x^2.
What is f'(x)=3x?
300
Find dy/dx given xy^3 +y^3+x^2=10
What is dy/dx=(-2x-y^2)/(2xy+3y^2)?
300
This is when and how you use the chain rule.
What is when you have a composition of two functions? What is when you take the derivative of the outside function and multiply that by the derivative of the inside function?
300
This is the behavior of a function when its first derivative is positive.
What is the function is increasing?
400
This is how you know the limit of a function exists when looking at its graph.
What is when the limit from the left equals the limit from the right?
400
This is the derivative of g(x)=(3-x^2)^1/2.
What is -x/((3-x^2)^1/2)
400
Given f'(x)=((x-2)^2)(x+3)(x-1), this is the interval on which f(x) is increasing.
What is (-infinity, -3) and (1, infinity)?
400
This is the behavior of a function when the second derivative is negative.
What is the function is concave down?
400
This is what you use to determine critical or inflection points in a function.
What is a sign chart?
500
This is how you determine if a piecewise function is continuous.
What is evaluate the transition domain values at both pieces and see if the outputs are equivalent.
500
If f(x)=(2x-1)/(x+1), find f'(1).
What is 3/4?
500
This is the location of the inflection point for f(x)=x^4+4x^3+6x^2+1.
What is this is a trick question with no inflection point?
500

This is the name of what occurs when the second derivative of a twice-differentiable function changes from a positive to negative or negative to positive.

What is an inflection point?

500
This is what you get when you evaluate the derivative at a given point or value.
What is the slope of the tangent line?
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