- #1
Qube
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Homework Statement
http://i.minus.com/jX32eXvLm6FGu.png
Homework Equations
The MVT applies if
1) The function is continuous on the closed interval [a,b] such that a<b.
2) The function is differentiable on the open interval (a,b)
And if the above two conditions are fulfilled then there is some point c between a and b at which the slope is equal to (f(b) - f(a)) / (b-a)
The Attempt at a Solution
1) The function is continuous for all real x. The function has a slope for all real x.
2) The function is differentiable for all x, as stated in the problem.
Therefore the MVT applies.
Because the MVT applies [f(7) - f(1)] / 6 = f'(c).
The maximum that f'(c) can be is 5, as stated in the problem. The slope is always between 2 and 5, including the endpoints. The minimum f'(c) can be is 2.
Therefore the inequality should be 12 ≤ f(7) - f(1) ≤ 30.
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