Graph of functions are given in the fol...

Graph of functions are given in the following figure. Check the functions for absolute extremum.

Text Solution

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(a) Function has no absolute minima nor absolute maxima.
(b) Function has absolute minima but no absolute maxima.
(c) Function has local maxima at x = 0 as `f(0 - h) f(0+h) lt f(0) (=2)`.

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Which of the following function is even function

`f(x)=(a^x+1)/(a^x-1)`

`f(x)=x((a^x-1)/(a^x+1))`

`f(x)=(a^x -a^(-x))/(a^x + a^(-x))`

f(x) = sin x

The function f(x)=sinxcos^(2)x has extremum at -

`x=(pi)/(2)`

`x=cos^(-1)((1)/(sqrt(3)))`

`x=cos^(-1)(sqrt((2)/(3)))`

`x=cos^(-1)(-sqrt((2)/(3)))`

In a given interval a function-

can have two consecutive maxima

can have two consecutive minima

possesses maximum and minimum values alternately

cannot have more than two extreme values.