anonymous
  • anonymous
Show that the function f(x) = x4 + 3x + 1 has exactly one zero on the interval [−2,−1].
Mathematics
schrodinger
  • schrodinger
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abb0t
  • abb0t
Take the derivative.
anonymous
  • anonymous
MVT
anonymous
  • anonymous
afterthat what can we proof is there a 0 point between domain

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anonymous
  • anonymous
how can sorry
anonymous
  • anonymous
can you explain the solution by writing step by step? :) it's urgent :(
cwrw238
  • cwrw238
derivative is 4x^3 + 3 4x^3 + 3 < 0 for negative gradient x^3 < -3/4 x < (-3/4)^(1/3) = approx -0.9 this is greater than -1 so the graph is decreasing over the period -2,-1 find value of function atx = -2 and -1 f(-2) = (-2)^4 + 3(-2) + 1 = 11 f(-1) = -2 meaning it has crossed the x-axis at most once over the period
anonymous
  • anonymous
thank u for solution crw238 :)

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