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is it b? I am rust on my calc I
have't done those in years
those re in the book in a highlighted box to remember for sure
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).
because f" in relation to f' is same as f' in relation to f. (one way to think about it)
So A would have been true, if it sais "concave up".
[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.
just remember, the derivative is just a instantaneous rate of change, the slope of a tangent line to a curve... that should work
+ derivative, the function has positive sloped tangents, it must be going upwards
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.
is that most of calc, how the heck do you calculate a slope of a line with 1 point
What do you realy mean?
infinitesmals i guess a distance vanashing, so really you have a slope from one point, maybe
(If I am interpreting the question correctly, if not nvm) We are considering the case in option C as given.
If you have any questions ask them piz.
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