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chichilove82
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$1.00 Continuous 1

  • From Mathematics: Algebra
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  • Due on Apr. 22, 2008
  • Asked on Apr 17, 2008 at 10:00:41PM
Q:
Suppose that the function f is continuous on [a,b], x_1 and x_2 are in [a,b], and k_1 and k_2 are positive real constants. Prove that there exists c between x_1 and x_2 for which
f(c)=[k_1 f(x_1)+k_2 f(x_2)]\[k_1+k_2]




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cxxliu
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$1.00 intermediate value again

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  • Posted on Apr 18, 2008 at 2:03:57PM
A:
Preview: ... k_1 f(x_1) + k_2 f(x_2)) / (k_1+k_2). It is easy to see that f(x_1) <= y <= f(x_2):<br><br>y >= (k_1 f(x_1) + k_2 f(x_1)) ...

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