Let us learn about maxima and minima
A function is refers to be monotonic if it is either increasing or decreasing but not both in a given interval.
Consider the function f(x) = 3x+1, x£ [0,1]
The mentioned function is increasing function on R. Hence continuous function is a monotonic function in [0, 1]. Continuous function has its minimum value at x = 0 that is equal to f (0) =1, has a maximum value at x = 1, that is equal to f (1) = 4.
'Every monotonic function imagines its maximum or minimum values at the end points of its domain of definition.'
Point to be remember that 'every continuous function on a closed interval has a maximum and a minimum value
The maxima and minima value of an expression or quantity is meant primarily the "greatest" or "least" value which it can receive. However, there are notes at which its value ceases to increase & begins to decrease; its value at such a point is known a maximum. So there are points at that its value ceases to decrease & begins to increase; such a value is known as a minimum. There may be many maxima or minima, & a minimum is not necessarily less than a maximum. For illustration the expression (x 2 -1x+ 2)/(x - 1) can driven all values from - 00 to - 1 & from + 7 to + oo, but has, so long as x is real, no value between - 1 & + 7. Here - 1 is a maximum value, & + 7 is a minimum value of the expression, though it can be made greater or less than any assignable quantity.
In our next blog we shall learn about interval world I hope the above explanation was useful.Keep reading and leave your comments.
A function is refers to be monotonic if it is either increasing or decreasing but not both in a given interval.
Consider the function f(x) = 3x+1, x£ [0,1]
The mentioned function is increasing function on R. Hence continuous function is a monotonic function in [0, 1]. Continuous function has its minimum value at x = 0 that is equal to f (0) =1, has a maximum value at x = 1, that is equal to f (1) = 4.
'Every monotonic function imagines its maximum or minimum values at the end points of its domain of definition.'
Point to be remember that 'every continuous function on a closed interval has a maximum and a minimum value
The maxima and minima value of an expression or quantity is meant primarily the "greatest" or "least" value which it can receive. However, there are notes at which its value ceases to increase & begins to decrease; its value at such a point is known a maximum. So there are points at that its value ceases to decrease & begins to increase; such a value is known as a minimum. There may be many maxima or minima, & a minimum is not necessarily less than a maximum. For illustration the expression (x 2 -1x+ 2)/(x - 1) can driven all values from - 00 to - 1 & from + 7 to + oo, but has, so long as x is real, no value between - 1 & + 7. Here - 1 is a maximum value, & + 7 is a minimum value of the expression, though it can be made greater or less than any assignable quantity.
In our next blog we shall learn about interval world I hope the above explanation was useful.Keep reading and leave your comments.
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