MAXIMUM AND MINIMUM

Question	Answer
1. Compare the graphics of the following functions, then prove the resulted inequality. a) f (x) = ln (x + 1) and g (x) = x, ∀x∈(-1,∞) b) f (x) = sin x, g (x) = x, ∀x∈[0,∞).	2. Find the point on the graph of the function f(x)=2√x which is situated at a minimal distance from the point A(2,0).
3. Having a rectangular box with dimensions of 10 cm and 20 cm, cut a square out of each corner, each the same size, so that by folding to obtain a rectangular box whose volume is the largest.	4. A company will employ some workers to install 800 alarms to cars. A worker is paid 20 € per hour and can install 5 alarms per hour. The company also pays health insurance of 100€ for each worker hired. How many workers should the company hire so as the costs be minimal.
5. On the sides of the rectangle ABCD, with AB=a and BC=b, there are four points: M, N, P, Q such as AM = BN = CP = DQ = x. Which is the minimum area of the MNPQ parallelogram when x varies. Image: 1fdf1826-6d77-4084-bd23-680bd7f4c127 (image/jpg)	Fermat's Theorem Let f :(a,b)-R be a function and suppose that z is a local extremum of f . If f is differentiable at z , then f'(z)=0. Image: b5772964-a44e-4d0f-9538-a2db0ebcd80d.gif (image/gif)

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	Created by Daniela Burtoiu almost 9 years ago