Chapter 3 - Definitions Flashcards
What is the definition for a critical point?
Let f go from D to the real numbers, be differentiable. Then c in D is a critical point of f if f’(c)=0
What is the definition for increasing?
for f going from D to the real numbers is increasing if for all x,y in D with x less than y, f(x) is less than or equal to f(y)
What is the definition for strictly increasing?
for f going from D to the real numbers is strictly increasing if for all x,y in D with x less than y, f(x) is less than f(y)
What is the definition for decreasing?
for f going from D to the real numbers is decreasing if for all x,y in D with x less than y, f(x) is greater than or equal to f(y)
What is the definition for strictly decreasing?
for f going from D to the real numbers is strictly decreasing if for all x,y in D with x less than y, f(x) is greater than f(y)
What is the definition for a function to be continuously differentiable and for it to be continuously differentiable? Then say what these set of functions are denoted by.
A function f that goes from D to the real numbers is continuously differentiable if it is differentiable and the derivative of f that goes from D to the real numbers is continuous.
It is n times continuously differentiable if all its derivatives up to the nth exist everywhere on D, and are continuous.
Th set of such functions are denoted by C with index n and D in brackets.
“f is in C to the power of n” if f is in C with the index n and D in brackets.
What is the definition for a function to be smooth and what is it denoted by?
The function f is smooth if it is C to the power of n for all n in the positive integers.
The set of smooth functions is denoted C with the index infinity and D in brackets.
What is the set of continuous functions, D goes to the real numbers, denoted by?
C with the index 0 and D in brackets
