Calculus: Extreme Values Quiz

What is the absolute maximum of a function over an interval?

• The smallest value

• The largest value

• The value at a critical point

• Always zero

The Extreme Value Theorem applies only when the function is:

• Continuous over an open interval

• Continuous over a closed, bounded interval

• Discontinuous

• Undefined

An absolute minimum can occur:

• Only at endpoints

• Only at critical points

• At endpoints or critical points

• Nowhere

If a function is not continuous over a closed interval, it may:

• Still have absolute extrema

• Not have absolute extrema

• Always have a minimum

• Always have a maximum

A local maximum occurs at c if:

• f(c) ≥ f(x) for all x near c

• f(c) ≤ f(x) for all x near c

• f(c) is undefined

• f'(c) is always positive

A critical point of f is where:

• f′(c)>0

• f′(c)<0

• f′(c)=0 or f′(c)f'(c) is undefined

• f(c)=0

According to Fermat’s theorem, if ff has a local extremum at c and is differentiable there, then:

• f′(c)=0

• f′(c)>0

• f′(c)<0

• f′(c) is undefined

All critical points are:

• Local maxima

• Local minima

• Candidates for extrema

• Absolute extrema

To find absolute extrema on a closed interval, you evaluate:

• Only at endpoints

• Only at critical points

• Endpoints and critical points

• At zero

If a function’s derivative does not exist at a point, this point:

• Cannot be critical

• Must be an endpoint

• Can still be a critical point

• Must be a maximum