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anonymous
 5 years ago
what is a sign graph and how do i draw one for 3x^24x+2 for F'(x)
anonymous
 5 years ago
what is a sign graph and how do i draw one for 3x^24x+2 for F'(x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sign graphs are annoying. it is easier to find the zeros of \[3x^24x+2\] if any and then recall that the graph of \[y=3x^24x+2\] is a parabola that faces upwards, so it will be positive outside the zeros and negative between them (from the picture).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0unless i am not paying attention it looks like this does not have any zeros. \[b^24ac=(4)^4\times 3\times 2 = 1624= 8\] so no real zeros. means the parabola is always above the x axis and so always positive. if this is a derivative of something, then that something must always be increasing. check my work because i might have made an arithmetic mistake.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sign graphs are an excellent tool. For example in this case, find derivative f'(x) = 6x^24. Find critical points 3x^22=0 3x^2=2 x^2=2/3 x=sq rt (2/3) So you evaluate from negative infinity to critical point and from critical point to positive infinity. Plug in any number between negative infinity to critical point to find if it is positive or negative within integral.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i suppose. but if \[3x^22=0\] \[3x^2=2\] \[x^2=\frac{3}{2}\] then there are two zeros, \[x=\sqrt{\frac{6}{2}}\] and \[x=\sqrt{\frac{6}{2}}\] don't need to test anything, since we know \[y=3x^22\] is a parabola facing up, negative between zeros and positive outside them. guess it is just a matter of taste.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0a sign graph i believe is the numberline marked out for + and  regions right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0<...............(c)..............>  + slope is decreasing when (); amd increaseing when (+)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and (c) is the zero of f'(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, usually you stack the factors up x1                       + + + + + + + x+3       + + + + + + + + + + + + + + + + + + _________3______________1__________ +  + looks something like the above

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i perfer the stacking; makes it simpler :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, it is bookkeeping, where you can list behavior of f(x), f'(x) and f''(x). It is not a big deal, but for someone learning calculus, this subject is overwhelming and it is a good way to read the graph.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the second derivatives sigh chart tells you concavity and inflection...right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0are there any intriguing details for higher derivatives?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i will not argue that point, but it is also good to know in advance what a quadratic looks like, what a cubic looks like etc, so you don't have to reinvent the wheel each time. yes second derivative gives concavity.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0third derivative is sometimes called "jerk" as it is the rate of change of the acceleration (assuming your original function is the position function, so first derivative is velocity and second is acceleration)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0hunh... give medal changed to good answer :) more descriptive i spose of its intent lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its good to know, i think, that 1st derivative zeros can give false readings; in the case where an inflection point has a 0 slope to it
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