Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). If
f(a)=f(b)
then there is at least one number c in (a,b) such that f'(c)=0.
What is Rolle's Theorem
100
Tests for relative maximums or minimums.
What is the First Derivative Test?
100
begins with l and ends with s
What is l-i-m-i-t-s
200
-cos(X)
What is derivative of sin(x)?
200
the absolute min and max
What is the min and max on a closed interval?
200
This person is a French mathematician who wrote Rolle's Theorem.
Who is Michel Rolle?
200
if f' crosses the x axis at 3 going from negative to positive then f has a ______ ______ at 3
What is a relative minimum
200
A line that touches the graph at one point
What is a tangent line
300
34x^33+1/2
What is the derivative of x^34+x/2 -5
300
a maxima
What is the plural of a maximum?
300
If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b) then there exists a number c in (a,b) such that
f(b)-f(a)
f'(c)= ______
b-a
What is the Mean Value Theorem.
300
if f" crosses the x axis then f has a ______ _____ ______
What is point of inflection
300
The line y=L is a _____ ______ of the graph of f if
lim lim
x->-INF f(x)=L or x->INF f(x)=L
What is horizontal asymptote
400
Strive for
What is 5
400
Let "F" be defined at c. If f'(c)= 0 or if f is not differentiable at c, then c is a critical number of f.
What is the definition of a critical number?
400
This mathematician wrote the Mean Value Theorem.
Who is Joseph-Louis Lagrange?
400
If f"(c) > 0
then f(c) is _____ _____
What is concave upward
400
Where did Sudbury graduate from?
What is the University of Pittsburgh
500
engineering
What is being done with calculus
500
Pierre De Fermat
Who wrote many of the fundamental theorem of calculus before Newton?
500
f(b)=f(a)+(b-a)f'(c).
What is the alternative form of Mean Value Theorem?
500
If f"(c)<0
then f(c) is ______ ______
What is concave downward
500
One of a handful of women to receive credit for significant contributions to mathematics before the twentieth century.