# Derivation - examples

- Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Derivation

Exists a function whose derivation is the same function? - Fall

The body was thrown vertically upward at speed v_{0}= 46 m/s. Body height versus time describe equation ?. What is the maximum height body reach? - Statue

On the pedestal high 2.3 m is statue 3.3 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.5 m. - Goat

Meadow is a circle with radius r = 22 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow? - Minimum of sum

Find a positive number that the sum of the number and its inverted value was minimal. - Paper box

Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box? - Sphere in cone

A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions. - Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m^{3}to have painted/bricked walls with least amount of material. - Cone

Into rotating cone with dimensions r = 18 cm and h = 17 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder. - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag - Sphere and cone

Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?

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