Chapter 6
Show that the function given by f (x) = 3x + 17 is increasing on R.
Prove that the logarithmic function is increasing on (0, ∞).
Prove that the function f given by f(x) = x2 - x + 1 is neither strictly increasing nor decreasing on (- 1, 1).
Which of the following functions are decreasing on 0, 2 π ? (A) cos x (B) cos 2x (C) cos 3x (D) tan x
On which of the following intervals is the function f given by f (x) = x100 + sin x -1 decreasing ? (A) (0,1) (B) ,2 π π (C) 0, 2 π (D) None of these
For what values of a the function f given by f (x) = x2 + ax + 1 is increasing on [1, 2]?
Let I be any interval disjoint from [-1, 1]. Prove that the function f given by 1( )f x x x= + is increasing on I.
Prove that the function f given by f (x) = log sin x is increasing on 0 2, π and decreasing on π π2 , .
Prove that the function f given by f (x) = log |cos x| is decreasing on 0, 2 π and increasing on 3 , 22 π π .
Prove that the function given by f (x) = x3 - 3x2 + 3x - 100 is increasing in R.
The interval in which y = x2 e-x is increasing is (A) (- ∞, ∞) (B) (- 2, 0) (C) (2, ∞) (D) (0, 2)
Show that the function given by f (x) = e2x is increasing on R.
Show that the function given by f (x) = sin x is (a) increasing in 0, 2 π (b) decreasing in ,2 π π (c) neither increasing nor decreasing in (0, π)
Find the intervals in which the function f given by f (x) = 2x2 - 3x is (a) increasing (b) decreasing
Find the intervals in which the function f given by f(x) = 2x3 - 3x2 - 36x + 7 is (a) increasing (b) decreasing
Find the intervals in which the following functions are strictly increasing or decreasing: (a) x2 + 2x - 5 (b) 10 - 6 / x - 2x2 (c) -2x3 - 9x2 - 12x + 1 (d) 6 - 9x - x2 (e) (x + 1) 3 (x - 3) 3
Show that 2log(1 ) 2 xy x x= + − + , x > - 1, is an increasing function of x throughout its domain.
Find the values of x for which y = [x(x - 2)]2 is an increasing function.
Prove that 4sin (2 cos )y θ= − θ+ θ is an increasing function of θ in 0 2, π .