It states: Every function which is continuous in a closed domain possesses a maximum and minimum Value either in the interior or on the boundary of the domain . The proof is by contradiction.
What are the conditions of maxima and minima in case of two variables?
Maxima/minima occur when f (x) = 0 . x = a is a maximum if f (a) = 0 and f (a) < 0; • x = a is a minimum if f (a) = 0 and f (a) > 0; A point where f (a) = 0 and f (a) = 0 is called a point of inflection.
What are the conditions for maximum?
To find whether f has a maximum or minimum at a critical point you must look to the quadratic approximation (or if necessary to the first higher approximation at which f deviates from flatness) to f . If its second derivative is positive then, like x 2 , f has a minimum at q , and if it is negative f has a maximum.
What is the condition of minimum?
A prism is said to be in minimum deviation position when the angle of incidence at the 1st surface is equal to the angle of emergence at the second surface . In such a condition, the rays travel parallel to the base inside the prism.
Which work done is maximum?
Hence, work done is maximum when θ is at zero degrees . (ii) Work done is minimum when the Force and Displacement are perpendicular to each other.
In which case work done is maximum?
when work done is maximum if force and displacement in the same direction w=FS . the work done is minimum if force and displacement perpendicular to each other.
How do you calculate maxima minima?
- Given f(x), we differentiate once to find f ‘(x).
- Set f ‘(x)=0 and solve for x. Using our above observation, the x values we find are the ‘x-coordinates’ of our maxima and minima.
- Substitute these x-values back into f(x).
What is maxima and minima in YDSE?
Now, dark fringes are formed in YDSE on the screen whenever there is a minima or destructive interference between the two interfering light rays emanating from the slits. ... However, there is nothing such as the central minima in YDSE. The minima next to the central maxima is the first minima.
What is the drawback of Lagrange’s method of maxima and minima?
Explanation: In lagrange’s theorem of maxima of minima one can not determine the nature of stationary points .
In which condition f/c is neither a maximum nor a minimum?
if f changes sign from negative to positive at c, then f has a local minimum at c. if f does not change sign at c, then f(c) is neither a local maximum nor minimum. Example: Let f(x) = x3 + 4×2 − 3x + 1.
In which conditions does minimum deviation occur?
Light is deflected as it enters a material with refractive index . A ray of light is deflected twice in a prism. The sum of these deflections is the deviation angle. When the entrance and exit angles are equal , the deviation angle of a ray passing through a prism will be a minimum.
What is minimum in math term?
Minimum, in mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum); see extremum.
Which work done is maximum adiabatic or isothermal?
In the isothermal process, the heat is given by surrounding for work done whereas the heat change is zero in the adiabatic process so, the work done in the isothermal process is greater than the work done in the adiabatic process.
What is dF DQ?
Why dF/dq is equal to zero for the force to be maximum in the problem below: A charge Q is divided into two parts of qand Q-q if the coulomb repulsion between them when they are seprated is to be maximum the ratio of Q/q should be.
How do you calculate minimum work?
If minimum work is done, it means that the object has minimum energy at the top of the staircase. As potential energy can’t be zero due to work done by gravity, the only possibility is that kinetic energy is 0. Thus work done =mg*height raised .
What is maximum and minimum work?
Work is said to be done when applied force is able to produce some displacement. If the applied force is in one direction and the displacement of the body is in the opposite direction, then work done is minimum as COS 180 is equal to minus one . ...
