To infinity
and beyond
and beyond
This is when you look at the behavior of a function f close to a value a but only looking at numbers that are less than a
What is the left hand limit of f as x approaches a?
This is the derivative of the n-th power of x
What is nx^(n-1)?
This is given by y=mx+b
What is the equation of a line in slope-intercept form?
This theorem guarantees that if a function is continuous in [a,b] then it must have an absolute maximum and an absolute minimum
What is the Extreme Value Theorem?
This is what you do to find critical points
What is finding the values when f'(x)=0 or DNE?
This is when the limit of f as x approaches a equals infinity
What is a vertical asymptote at a?
This is the slope of the tangent line to a curve at a given point
What is the derivative?
They are x=2 and y=0 for the function 1/(x-2)
What are the vertical and horizontal asymptotes of the function?
This theorem says that if a function is continuous in [a,b], then there is a value c in (a,b) with slope given by the quotient of f(a)-f(b) and a-b
What is the Mean Value Theorem?
Optimization problems usually require you to check critical points and this to find the solution
What are the endpoints?
It is the value that a function f is approaching when x is a number close to a but different than a
What is the limit of f as x tends to a?
This is the derivative of a position function with respect to the time
What is velocity?
This is given by x when x is positive or 0, and -x when x is negative
What is the definition of |x|?
This theorem says that a function that is continuous in [a,b] then it takes all the values between f(a) and f(b)
What is the Intermediate Value Theorem?
Both the First Derivative and Second Derivative test help determine if a critical point is this
For a function f at a point a, you need the limit as x approaches a and f(a) to agree
What is the definition of continuity?
This is when you find an expression for y' without necessarily solving for y first
What is implicit differentiation?
This is the linear approximation of a function f at a point a
What is y=f(a)+f'(a)(x-a)?
This is a particular case of the MVT when the two endpoints have the same value of f
What is Rolle's Theorem?
This happens when f''<0
What is concave down?
These are the inequalities in the formal definition of a limit when f approaches L as x approaches a
What are |f(x)-L|<epsilon and |x-a|<delta?
What is logarithmic differentiation?
One is the difference between the values of a function, and the other is the difference between the values of its approximation
What is the difference between Δy and dy?
This theorem is used to find out what the limit of g is when you already know what the limits of f and h are at a given point, assuming f is less or equal to g and g is less or equal to h
What is the squeeze theorem?
When s is the position function, this happens when s'>0 and s''<0
What is slowing down?