Calculus Help
Which of the following are true?
Every absolute minimum is a local minimum.
If f is continuous on a closed interval (ab), then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (ab).
If f(c)=0, the f has a local maximum or minimum at c.
The function f(x)=x has no critical points on the interval (negative5,5).
If f has a local maximum or minimum at c, then c is a critical number of f.
If f has an absolute minimum value at c, then f(c)=0.
November 12, 2013
4 Comments • Newest first
last and 3rd one are false. @ness got this under control.
[quote=Blackyoshi]Every absolute minimum is a local minimum.[/quote]
True.
[quote=Blackyoshi]If f is continuous on a closed interval (ab), then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in (ab).[/quote]
True.
[quote=Blackyoshi]If f(c)=0, the f has a local maximum or minimum at c.[/quote]
False. This is true if f'(c) = 0.
[quote=Blackyoshi]The function f(x)=x has no critical points on the interval (negative5,5).[/quote]
True.
[quote=Blackyoshi]If f has a local maximum or minimum at c, then c is a critical number of f.[/quote]
True.
[quote=Blackyoshi]If f has an absolute minimum value at c, then f(c)=0.[/quote]
False. This is true if f'(c) = 0.
The first is true.
I don't think the second is always true.
Third isn't true.
Fourth is true. (I'm not really sure, actually. If the line goes from (-5,-5) to (5,5) then the slope is never 0, right?)
Fifth is true.
Sixth is true.
I haven't taken calc 1 since high school. The points at which f'(x) = 0 are critical points right? Max and mins can only be at critical points right? If I'm right on both of these things, then the answers I gave you are right.
Every absolute minimum is a local minimum - False...? If it's an absolute minimum, then it's the lowest possible point on the graph. All other minimum are classified as local minimum. The same applies for Maximum.
Perhaps I'm wrong though. I myself am struggling with Calculus. Would appreciate it someone can confirm this... and explain the rest of OP's questions, haha.