CALC

Question 1

Absolute maximum value

Answer 1

which is when f(c) is the largest value that f attains across the entire domain.

textbook:

absolute maximum value of f on D if f(c) ≥ f(x) for all x in D

D = domain

Question 2

Absolute minimum value

Answer 2

which is when f(c) is the smallest value that f attains across the entire domain.

absolute minimum value of f on D if
f(c) ≤ f(x) for all x in D

D = domain

Question 3

local maximum value

Answer 3

of f if f(c) ≥ f(x) when x is near c

Question 4

local minimum value

Answer 4

of f if f(c) ≤ f(x) when x is near c

Question 5

Extreme Value theorem

Answer 5

If f is continuous on a closed interval [a,b], then f has an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a,b]