Q1 of 105 Page 17

Mark the correct alternative in the following:

The interval of increase of the function f(x) = x – ex + tan is


Formula:- The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)


Given:-




Now


f’(x)>0


1-e


x>0


X<0


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38

Let F defined on [0, 1] be twice differentiable such that | f”(x) ≤ 1 for all x ϵ [0, 1]. If f(0) = f(1), then show that |f’(x) | < 1 for all x ϵ [0, 1] ?

 39

Find the intervals in which f(x) is increasing or decreasing :

i. f(x) = x |x|, x ϵ R


ii. f(x) = sin x + |sin x|, 0 < x ≤ 2 π


iii. f(x) = sin x (1 + cos x), 0 < x < π/2

 2

Mark the correct alternative in the following:

The function f(x) = cos–1 x + x increases in the interval.


 3

Mark the correct alternative in the following:

The function f(x) = xx decreases on the interval.