anonymous
  • anonymous
f(x) = 1/2 x^4 - x^2 +5 find the global maximum and the global minimum values of f(x) (if they exist) on [0,2] please and thank you!
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Procedure: Find stationary points, that is points at which the gradient is zero i.e. f'(x)=0 such that x is in [0,2] Determine for each of these whether they are maxima or minima through use of the second derivative. Differentiating: \[f'(x) = 2x^3-2x\] Solving for f'(x)=0 we get x=0,1 in [0,2] \[f''(x) = 6x^2-2\] f''(0) = -2 < 0 implies that 0 is a maximum point. f''(1) = 4 > 0 implies that 1 is a minimum point. We are done. Ask for clarification is necessary.
anonymous
  • anonymous
thank you so much!

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