Derivation - practice problems
Number of problems found: 42
- A particle 2
If the motion of a particle is described by the relation a(t) = 7t³ + 2 m/s², and the initial velocity of the motion is zero when t = 0 and the distance is 2m, t = 0.5s. Determine the velocity and displacement when t = 10s.
- Parabola with abs
A). Sketch the graph of the function f(x)=x * absolute(x) = x * |x| b). For what values of x is f(x) differentiable c). Find f'(x)
- Intersection of Q2 with 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. (ii) show that one of these points is also the
- Function x*tanx
Functions: f(x)=xtanx f(x)=(e^x)/((e^x)+1) Find; i)vertical and horizontal assyptotes iii)the interval of decrease and increase iii)Local maxima and local minima iv)interval of concavity and inflection. And sketch the graph.
- The MRT train
The MRT running from Taft to North Avenue has a starting velocity of 60km/hr. After a malfunction, the brakes failed, making the train run with a velocity of 80km/hr. What is the acceleration rate if the time for velocity change is 5 seconds?
- Penny free fall
A man drops a penny from the top of a 500m tall building. After t seconds, the penny has fallen a distance of s metres, where s(t)=500-5t² . Determine the average velocity between 1s and 5s .
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?
- Sleep vs. watch TV time
Using a data set relating about number of episodes I watch of TV in a day (x) versus number of hours of sleep I get that night (y), I construct the linear model y=−0.6x+11 Which of the following is a general observation that you can make from this model?
- Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
- The shooter
The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most likely num
- Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
- Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 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 = 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
- 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 t hours after administration: c (t) = -0.025 t ^ 2 + 1.8t. When will the liver product be eliminated entirely?
- The position
The position of a body at any time T is given by the displacement function S=t³-2t²-4t-8. 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?