THEOREMS
You can classify a critical point as a min or a max based on a change in the sign of f'
What is the First Derivative Test?
17th century English genius; central figure in Calculus
Who was Isaac Newton?
d/dx( ? ) = 3x2
What is x3?
The sign of f' when f is increasing
What is positive?
What is the limit of 3x2 / x3 as x approaches infinity?
What is zero?
If f(c) is a min or max, then c is a critical point of f
What is Fermat's Theorem?
17th century German; central figure in Calculus
Who was Gottfried Leibniz?
d/dx( ? ) = 1/x
What is ln x?
The sign of f'' when f is concave down
What is negative?
What is the limit of sin(3x) / 3x as x approaches 0?
What is one?
You can classify a critical point as a min or max based on the sign of f''
What is the Second Derivative Test?
17th century French; preceded Newton; has a theorem with his name; not Pascal
Who was Pierre Fermat?
d/dx( ? ) = 4x ln 4
What is 4x ?
f(c) has a ___________ when f'(c) = 0 and f' changes from - to + at c
What is a minimum?
What is the limit of [1 - cos(x)] / x as x approaches 0?
What is zero?
Helps you to calculate indeterminate limits in the form a/b
What is L'Hopital's Rule?
17th century French; came after Newton; wrote the first Calculus textbook
Who was L'Hopital?
d/dx( ? ) = - csc x cot x
What is csc x?
When f' is decreasing, f is _________________
What is concave down?
What is the limit of 2x / x3 as x approaches infinity?
What is infinity or does not exist?
States that on an interval there must be a tangent line that is parallel to the secant line on the interval
What is the Mean Value Theorem?
Brilliant Swiss family with several mathematicians, including Johann and Jakob, in the 17th and 18th centuries
Who were the Bernoullis?
d/dx( ? ) =1/sqrt(1-x^2)
What is sin-1x?
When f''(c) is undefined, f'' < 0 to the left of c and f'' > 0 to the right of c, c is a _____________________
What is a point of inflection?
What is the limit of x / ln(x) as x approaches infinity?
What is infinity or does not exist?