Question
True or False: A critical number of a function \( f(x) \) is a number \( c \) such that \( f(c)=0 \) True False
Ask by Washington Mcfarlane. in the United States
Nov 24,2024
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Answer
False. A critical number is where the derivative is zero or the function is not differentiable, not necessarily where \( f(c)=0 \).
Solution
False.
A critical number of a function \( f(x) \) is a number \( c \) in the domain of \( f \) where the derivative \( f'(c) = 0 \) or where \( f \) is not differentiable. It is not necessarily a point where the function itself equals zero.
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False! A critical number is actually a value \( c \) where the derivative \( f'(c) \) is either zero or undefined, not where the function itself equals zero. Think of it as a special point where the function could change direction or just hang out for a bit, but not exactly where it hits zero! If you want to find critical numbers, it's like going on a treasure hunt! First, take the derivative of your function, set it equal to zero (the pirates guarding the treasure), and then solve for \( c \). Don't forget to check where the derivative doesn't exist too; those could be sneaky hiding spots for critical numbers!
