anonymous
  • anonymous
Consider x^2 on an interval [0,1/2]. The Mean Value theorem suggest that there is a number c in (0.1/1/2) such that f'(c) is equal to a particular d.What is d?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
find the slope of the secant line that passes through (.1, .01) and (.5, .25)
anonymous
  • anonymous
sorry, my browser crashed
anonymous
  • anonymous
is the interval [0, 1/2] or [0.1, 1/2]?

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anonymous
  • anonymous
well, I'll assume [0, 1/2] then. Let's say f(x) = x^2
anonymous
  • anonymous
Then the slope of the line between (0, f(0) and (.5, f(.5)) is (.25-0)/(.5-0) = 0.5
anonymous
  • anonymous
next find where the derivative equals 0.5. This is the point where the tangent line is parallel to the secant line between (0, f(0) and (.5, f(.5))
anonymous
  • anonymous
sorry I crashed too haha
anonymous
  • anonymous
so f'(x) = 2x = 0.5 x = 0.25
anonymous
  • anonymous
so is d 0.25?
anonymous
  • anonymous
yes
anonymous
  • anonymous
well, no actually
anonymous
  • anonymous
d is 0.5
anonymous
  • anonymous
oh k, that makes more sense
anonymous
  • anonymous
because f'(0.25) = 0.5 so c = 0.25 d = 0.5
anonymous
  • anonymous
thanks a lot
anonymous
  • anonymous
no problem

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