chris215
  • chris215
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Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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caozeyuan
  • caozeyuan
is it b? I am rust on my calc I
caozeyuan
  • caozeyuan
have't done those in years
DanJS
  • DanJS
those re in the book in a highlighted box to remember for sure

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SolomonZelman
  • SolomonZelman
If f'(x)>0 on interval (a,b) that means the function is increasing on (a,b). Consequentialy, if f''(x)>0, then the slope (f'(x)) is increasing on (a,b).
SolomonZelman
  • SolomonZelman
because f" in relation to f' is same as f' in relation to f. (one way to think about it)
SolomonZelman
  • SolomonZelman
So A would have been true, if it sais "concave up".
SolomonZelman
  • SolomonZelman
[option B] If f '(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). The slope is greater than zero, so yes, the function is increasing on that interval.
DanJS
  • DanJS
just remember, the derivative is just a instantaneous rate of change, the slope of a tangent line to a curve... that should work
DanJS
  • DanJS
+ derivative, the function has positive sloped tangents, it must be going upwards
SolomonZelman
  • SolomonZelman
If f '(c) = 0, then x = c is a relative maximum on the graph of f(x). Not necessarily! Could be absolute minumum for example.
DanJS
  • DanJS
is that most of calc, how the heck do you calculate a slope of a line with 1 point
SolomonZelman
  • SolomonZelman
What do you realy mean?
DanJS
  • DanJS
infinitesmals i guess a distance vanashing, so really you have a slope from one point, maybe
SolomonZelman
  • SolomonZelman
(If I am interpreting the question correctly, if not nvm) We are considering the case in option C as given.
SolomonZelman
  • SolomonZelman
If you have any questions ask them piz.
SolomonZelman
  • SolomonZelman
Oops, "pliz".
jim_thompson5910
  • jim_thompson5910
If f '(c) = 0, then the following is possible (only one can happen) * there is a relative min on f(x) at x = c * there is a relative max on f(x) at x = c * there is a saddle point on f(x) at x = c. A saddle point is a place where the tangent line has a slope of 0, but it's not a min or max this is why you have to use the first or second derivative test to figure out if there is an extrema at x = c
chris215
  • chris215
thanks!!

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