Working Rule to Check Whether a Differentable Function is Increasing or Decresing
(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the function (3) Arrange these Critical values in a..
The number of students opting for Japanese and French in a school are ..
The number of students opting for Japanese and French in a school are 60 and 281 respectively. The number of students opting for Japanese has been increasing at the rate of 6 students per year and that for French has been decreasing at the rate of 11 students per year. How long ..
1) Vasodilation and increased permeability of blood vessels
Vasodilation increases blood supply to the damaged area which will help to remove toxic products and dead cells. Increased permeability of blood vessels permits white blood cells and serum proteins to enter into the injured area. These changes occur due to release of ..
Select each study as being either observational(O) or experimental(E)...
Select each study as being either observational(O) or experimental(E). I. Children's behaviour in a play ground (aggression). II. Violence in children's TV programmes. III. Does fluoride in the water supply decrease the frequency of dental cases in a community compared to a simi..
An increase in pressure on a system where a liquid-vapour equilibrium exists
According to the Le Chatelier's principle, this will make the system move in a direction of lower volume. An increase in pressure on the system will result in the condensation of vapours to give liquid, since, liquids have lower volume as compared to vapours. The equilibrium will shift t..
The length and the width of a rectangle are 12 cm and 10 cm respective..
The length and the width of a rectangle are 12 cm and 10 cm respectively. If the length is increased by 3 and the width is increased by 2, how is the area changed? => increased by 60 cm 2 or increased by 30 cm 2 or decreased by 60 cm 2 or decre..
Alice is an athlete and has won many trophies. The number of trophies ..
Alice is an athlete and has won many trophies. The number of trophies she won in 3 rd , 4 th and 5 th grades is 4, 4 and 4. Will the number of trophies that she might win in her 6 th grade, increase, decrease or remain the same? => Increase or Decrease or Rem..
The oxygen percent decreases as the elevation increases. If h represen..
The oxygen percent decreases as the elevation increases. If h represents the elevation, find the oxygen percentage that shows the compound inequality 25000 < h ≤ 50000 from the table. => 14% or 6% or 50% or 35%..
Which of the following statement(s) is/are false?I. A relationship bet..
Which of the following statement(s) is/are false? I. A relationship between many variables is called multiple relationship. II. A relationship between three variables only is called multiple relationship. III. When both variables increase or decrease at the same time, then the r..
The height of a right circular cone is decreasing at the rate of 8 cm/..
The height of a right circular cone is decreasing at the rate of 8 cm/s and the radius of its base is increasing at the rate of 2 cm/s. Find the rate of change of volume of the cone when the height is 8 cm and the base radius is 2 cm. => 64 π cm³/s or 56 π cm³/s ..
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