(a) increasing in , (b) decreasing in (c) neither increasing nor decreasing in ( , π ) . Find the intervals in which the function f given by f ( x ) = x – x is (a) increasing (b) decreasing . Find the intervals in which the function f given by f ( x ) = x – x – x + is (a) increasing (b) decreasing . Find the intervals in which the following functions are strictly increasing or decreasing: (a) x + x – (b) – x – x (c) – x – x – x + (d) – x – x (e) ( x + ) ( x – ) .
Show that log( y , x > – , is an increasing function of x throughout its domain. . Find the values of x for which y = [ x ( x – )] is an increasing function. .
Prove that 4sin ( cos ) y θ −θ θ is an increasing function of θ in , π . . Prove that the logarithmic function is increasing on ( , ∞ ). .
Prove that the function f given by f ( x ) = x – x + is neither strictly increasing nor decreasing on (– , ). . Which of the following functions are decreasing on , ? (A) cos x (B) cos x (C) cos x (D) tan x .
On which of the following intervals is the function f given by f ( x ) = x + sin x – decreasing ? (A) ( , ) (B) (C) , (D) None of these . For what values of a the function f given by f ( x ) = x + ax + is increasing on [ , ]? .
Let I be any interval disjoint from [– , ].