anonymous
  • anonymous
is the graph y=sin(x^4) increasing or decreasing at x=10 and is it concave up or concave down
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Kira_Yamato
  • Kira_Yamato
y = sin (x^4) y' = 4 x^3 cos (x^4) y'(10) = 4000 cos (10000) cos 10000 = 0.17..... > 0 ==> y' > 0 ==> increasing
anonymous
  • anonymous
what about the convaveness
Kira_Yamato
  • Kira_Yamato
Find y''. If y'' (10) > 0, then it is concave up and vice versa. In this case, using product rule, y'' = 4 [(x^3)(4x^3)(-sin (x^4)) + (cos (x^4))(12x^2)] y'' = 4[12x^2 cos(x^4) - 4x^6 sin(x^4)] y'' = 48x^2 cos(x^4) - 16x^6 sin(x^4) y''(10) = 4800cos(10000) - 16000000sin(10000) y''(10) = 4 885 259.88... > 0 Since y''(10) > 0, concave up at x = 10

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anonymous
  • anonymous
THANKS!!!

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