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..Approximations by Differentials
Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..
Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..
Note 4:
dx and dy are called the differentials of x and y respectivel..
Solution:
Let y = f (x) = x 1 / 4 Let x = 81, d x =1. Taking these values we have ..
Let y = f (x) = x 1 / 4 Let x = 81, d x =1. Taking these values we have ..Example:
Sketch the curve y = - sin 2x ...
Passage through origin
Put x = 0, y = -sin2x = 0. This implies (0, 0) is a point on the curve or the curve passes through the origi..
Determination of Few Point
with this information, we sketch the graph as show ...
with this information, we sketch the graph as show ...Example:
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..Example:
Find the intervals on which the function (a) increasing (b) decreasing Differentiating the function, we have The critical values in ascending order are -1, 1. We divide the Real numbers into the intervals = - ve Since f '(x) < 0, the function is decreasing in the interval ..
Find the intervals on which the function (a) increasing (b) decreasing Differentiating the function, we have The critical values in ascending order are -1, 1. We divide the Real numbers into the intervals = - ve Since f '(x) < 0, the function is decreasing in the interval ..See what our Users say :
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