Derivation - practice problems - page 2 of 3
Directions: Solve each problem carefully. Show all your work.Number of problems found: 48
- Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Confectionery
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. - Drug liver elimination
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. - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can 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. - Function derivative
Calculate the value of the sixth derivative of this function: f (x) = 93x. - Fifth Derivative of Polynomial
Calculate the value of the fifth derivative of this function: f (x) = 3x² + 2x + 4 - Rectangle dimensions
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 of Linear Function
What is the value of the derivative of this function: f (x) = 12x - Derivative of Constant Function
Determine the value of the derivative of the function f (x) = 10 - Number division
Divide the number 28 into two summands so that their product is maximal. - Scooter income 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 the largest volume of the box be beside the squares? - Function continuity
Specify the point at which the sgn x function has no continuity. - Continuous function
Is there a continuous function that has no derivative at every point?
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