Question

when a question asks find an "extreme valve" what do we extally have to find ?

Answer 1

An extreme value in mathematics is any value which is either highest value (maximum) or the lowest value (minimum) in a given set of numbers. This is basically saying that when asked to find an "extreme value", you must find the greatest possible value and/or lowest possible value. The highest and lowest values are considered "extremes".

Answer 2

for local "extreme values", solve below :
\(f'(x) = 0 \)

Answer 3

for absolute "extreme values", take below :
absolute MAX = \(MAX \{\text{ all "local extreme values", boundary values }\} \)
absolute MIN = \(MIN \{\text{ all "local extreme values", boundary values }\} \)

Answer 4

you may use second derivative test if u want as well^^