Derivation - high school - practice problems - page 2 of 3
Number of problems found: 45
- Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Administration: 6982
The patient was given the drug, and the measured liver concentration was t hours after administration: c (t) = -0.025 t² + 1.8t. When will the liver product be eliminated entirely? - The position
The displacement function S=t³-2t²-4t-8 gives the position of a body at any time t. Find its acceleration at each instant time when the velocity is zero. - Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material. - Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal. - Derivative 4267
Calculate the value of the sixth derivative of this function: f (x) = 93x. - Derivative 4266
Calculate the value of the fifth derivative of this function: f (x) = 3x² + 2x + 4
- Circumference 4255
The rectangle has a circumference of 24 cm so that its area is maximum and its length is larger than its width. Find the dimensions of a rectangle. - Derivative 4251
What is the value of the derivative of this function: f (x) = 12x - Derivative 4239
Determine the value of the derivative of the function f (x) = 10 - Summands 4213
Divide the number 28 into two summands so that their product is maximal. - Manufacturer 4212
How many electronic scooters should the manufacturer sell to maximize their income if the income function is given by the equation TR (Q) = -4Q2 + 1280 Q + 350?
- Paper box
The hard rectangular paper has dimensions of 60 cm and 28 cm. We cut off the corners into equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box? - Continuity 4087
Specify the point at which the sgn x function has no continuity. - Derivative 4041
Is there a continuous function that has no derivative at every point? - Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - Goat
Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the Meadow's perimeter to allow the goat to eat half of the Meadow?
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