intervals of functions

We can take the value of f at a (i.e., f(a)) as first estimate for average value of the function. Divide [a, b] into two equal parts such that then the second estimate of the average value of the function can be taken as second estimate of the average value of the functionh..

A function f(x) is said to be continuous in an interval I, if it is continuous at each point of I. then x can approach c both from the left and the right and so for f (x) to be continuous at c, we must have If the interval I is the closed interval [a,b], then..

Choose the interval on which the function y = ( x + 2) 2 is increasing. => [- 2, ∞) or [- ∞, ∞] or (- ∞, - 2] or (- ∞, ∞)..

In which interval does the function y = 27 x + sin 4 x increase? => all real values of x or (- ∞, 0) or [0, ∞) or (0, ∞) or (27, ∞)..

Choose the interval on which the function y = | x + 2| + | x - 1| - 2 is decreasing. => [- 2, 2] or [- 2, ∞) or (- ∞, ∞) or (-∞, - 2]..

Periodic Functions - The trigonometric functions belong to a large class of functions called periodic functions in which there is a regular repetition of the values of the function over a certain interval..

A function is said to be monotonic if it is either increasing or decreasing but not both in a given interval. Consider the function The given function is increasing function on R. Therefore it is a monotonic function in [0,1]. It has it..

In which interval does the function f ( x ) = 2 x 3 - 3 x 2 - 12 x + 10 increase? => R - {0, 1, 2} or (- 1, 2) or (- ∞, - 1) ∪ (2, ∞) or (- ∞, - 1] ∪ [2, ∞) or (0, ∞)..

In which interval does the function f ( x ) = x 2 - 3 x - 2 x + 3 increase? => (- 3, ∞) or (- ∞, - 7] ∪ [1, ∞) or ( 7 3 , ∞) or (- ∞, - 7) ∪ (1, ∞) or (- 7, 1)..

Find the value in the interval, which satisfies the Mean Value Theorem for the function f ( x ) = 2 + x 3 on [- 1, 2]. => 0 or 1 1 3 or 2 or 1 or 3..