Derivative - practice problems - page 2 of 3

Directions: Solve each problem carefully. Show all your work.

Number of problems found: 45

Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000 m, 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 larg
Position vector of a point mass
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (t²+ 2t + 1 ; 2t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the positio
Position vector
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (1 + 5t + 2t² ; 3t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the posit
Vectors 5
The position vector of a material point moving in a plane can be expressed in the introduced reference frame by the relation: r(t) = (2t + 3t²; 6t + 3), where t is time in seconds and the coordinates of the vector are in metres. Calculate: a) what is the
Position vector of a point mass
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (6t²+ 4t ; 3t + 1) where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the position of
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.
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?
Ladder
A 4 m long ladder touches the cube 1mx1 m 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.
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 perimeter 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?
Continuous function
Is there a continuous function that is nowhere differentiable?

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