anonymous
  • anonymous
Guys, please Help me. I give medals. Which one of the following statements is true? -If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b). - If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). -If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x). -None of these are true.
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@ganeshie8 @dan815
anonymous
  • anonymous
@satelitte
anonymous
  • anonymous
@jim_thompson5910 @phi

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anonymous
  • anonymous
B is the answer. because c is wrong because if you have a slope of zero, it can be a max but it also can be a min. a is wrong because when you have concavity up, the f''x must be greater than zero and positive.
jim_thompson5910
  • jim_thompson5910
`If f ′(c) = 0, then x = c is a relative maximum on the graph of f(x)` there could be a relative min or a saddle point. So this statement is false.
jim_thompson5910
  • jim_thompson5910
`If f ′′(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b)` false. f(x) is concave up if the second derivative is positive
jim_thompson5910
  • jim_thompson5910
`If f ′(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b)` this is definitely true

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