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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
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find the slope of the secant line that passes through (.1, .01) and (.5, .25)
sorry, my browser crashed
is the interval [0, 1/2] or [0.1, 1/2]?

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Other answers:

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

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