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anonymous
 5 years ago
f(x) = x4  50x2 + 4
find the intervals on which f is increasing and decreasing. local min and max values. inflection points. intervals on which f is concave up and concave down.
anonymous
 5 years ago
f(x) = x4  50x2 + 4 find the intervals on which f is increasing and decreasing. local min and max values. inflection points. intervals on which f is concave up and concave down.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01st and 2nd derivatives give you all that information

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0y' = 4x^3 100x y'' = 12x^2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when y'=0 we get some critical points: y' = 4x^3  100x x(4x^2  100) = 0 x(2x10)(2x+10) = 0 x = 0, x=5, x=5 are all critical points to check <.......(5)......(0).......(5).......>

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0y'' = 12x^2 12(0)^2=0 ; good candidate for inflection 12(5)^2 = 12(25) which is (+), this is a MIN 12(5)^2 = 12(25) which is (+), this is ALSO a MIN <.......(5).......(0)........(5).......> 0++++(0)++++0> This thing is a big "W" looking graph with 5, 0, 5 being the low, high, low respectively

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(inf,0) concave up (0,inf) concave up (5,5) concave down :) depends on where you lookat it from I suppose

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0dont try to make any sense outta me line graph; it messed up anywhoos :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0decreasing (inf,5) increaseing (5,0) decreasing (0,5) increasing (5,inf)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0any of this making sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(5) = (5)^4  50(5)^2 + 4 = (5,621) MIN f(0) = 0  0 + 4 = (0,4) MAX f(5) = (5)^4  50(5)^2 + 4 = (5,621) MIN

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that should be all the answers :)
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