Maxima and Minima
Maxima and Minima - A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximum. Note that when 'a' is the point of loc..
Maxima and Minima - A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximum. Note that when 'a' is the point of loc..Maxima and Minima
A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximu..
A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that f(a) f(x) for all x I The number f(a) is called the local maximum of f(x). The point a is called the point of maximu..Ratio of Intensities at Maxima and Minima
It has already been proved that the intensity of a wave is proportional to the square of the amplitude. At a point where constructive interference has occurred, the intensity will be maximum and the amplitudes of the two waves will have added. If A 1 and A 2 are the amplitudes of the individual wav..
It has already been proved that the intensity of a wave is proportional to the square of the amplitude. At a point where constructive interference has occurred, the intensity will be maximum and the amplitudes of the two waves will have added. If A 1 and A 2 are the amplitudes of the individual wav..Step 2:
Solve f '(x) = 0 to get the critical values for f (x). Let these values be a, b, c. These are the points of maxima or minima. Arrange these values in ascending ord..
Conclusion Differentiation
Conclusion Differentiation - In this chapter, we have studied various techniques of differentiation. Also, we have studied the method of obtaining higher order derivatives of functions which is useful in maxima and minima problems.In this chapter, we have studied various techniq..
Optics Problems - Numerical 25
25. - Two coherent sources of intensity ratio 100:1 interfere. Deduce the ratio of intensity between the maxima and minima in the patter..
27.
The ratio of the intensities at minima to maxima in the interference pattern is 9:25. What will the ratio of the widths of the two slits be in Young's double slit experimen..
Numerical - 27
The ratio of the intensities at minima to maxima in the interference pattern is 9:25. What will the ratio of the widths of the two slits be in Young's double slit experimen..
CALCULUS
Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals ..
Example:
Find the local maxima or local minima, if any, for the following function using first derivative test f (x) = x 3 - 6x 2 + 9x +..
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