Fichas
MAXIMUM AND MINIMUM
Fichas del conjunto (3)
- 11. 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). - 23. 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.
- 35. 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.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.