Monday, February 8, 2010

Calculus Question: Is this statement true or false?

If f has one or more points of discontinuity on [a , b] or if f is not differentiable at every point of [a , b], then f has no relative extreme values on [a , b].





And can you please explain why you think it is true or false? I think it is false but I'd like to check. Thanks!Calculus Question: Is this statement true or false?
It is false. If a continuous region can be defined for that function, then the function can have relative extremes in that region. It can even have an extreme at a point of discontinuity, A function can have a value at a point of discontinuity, and if that value is greater or less than the value of nearby points, that is an extreme.Calculus Question: Is this statement true or false?
I'd say it's false. Look at the step function, y = [x], where the brackets here are the ';floor'; function. If you look at the closed interval [0,10], there are points of discontinuity at each of the integers, but there's still a relative maximum.
Differentiability across a domain subset only requires that the function is continuous, a step function across a step discontinuity is non-continuous, but it has extreme values none the less. I'd say false too.

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