Given: is strictly increasing if i.e., increasing on the interval is strictly decreasing if i.e., decreasing on the interval hence, is neither strictly increasing nor decreasing on...
Which of the following functions are strictly decreasing on (0,pi/2)
(C) (D) SOLUTION: (C) Since For Therefore, is strictly decreasing on For Therefore, is strictly increasing on Hence, is neither strictly increasing not strictly decreasing...
Which of the following functions are strictly decreasing on (0,pi/2)
(A) (B) SOLUTION: (A) Since in therefore Therefore, is strictly decreasing on (B) Since therefore Therefore, is strictly decreasing...
On which of the following intervals is the function f given by f(x)=x^100+sinx-1 is strictly decreasing:
(A) (0, 1) (B) (C) (D) None of these SOLUTION: Given: (A) On (0, 1), therefore And for (0, 1 radian) = > 0 Therefore, is strictly increasing on (0, 1). (B) For = = (1.5,...
Find the least value of a such that the function f given by f(x)=x^2+ax+1 strictly increasing on (1, 2).
Since is strictly increasing on (1, 2), therefore > 0 for all in (1, 2) On (1, 2) Minimum value of is and maximum value is Since > 0 for all in (1, 2) and and ...
Let I be any interval disjoint from [-1,1] Prove that the function f given by f(x)=x+1/x is strictly increasing on I.
Given: ……….(i) Here for every either or for , (say), > 0 And for , (say), > 0 > 0 for all , hence is strictly increasing on...
Prove that the function f given by f(x)=logsinx is strictly increasing on (0,pi/2) and strictly decreasing on (pi/2,pi)
Given: On the interval i.e., in first quadrant, > 0 Therefore, is strictly increasing on . On the interval i.e., in second quadrant, < 0 Therefore, is strictly decreasing...
Prove that the function f given by f(x)=logcosx is strictly decreasing on (0,pi/2) and strictly decreasing on (pi/2,pi)
Given: On the interval i.e., in first quadrant, is positive, thus < 0 Therefore, is strictly decreasing on . On the interval i.e., in second quadrant, is negative thus > 0...
Prove that the function given by f(x)=x^3-3x^2+3x-100 is increasing in R.
Given: for all in R. Therefore, is increasing on R.
The interval in which y=x^2e^(-x) is increasing in:
(A) (B) (C) (D) (0, 2) SOLUTION: Given: = = In option (D), for all in the interval (0, 2). Therefore, THE CORRECT OPTION IS option...
Prove that the logarithmic function is strictly increasing on (0,INFINITY)
Given: for all in Therefore, is strictly increasing on
Prove that (fig 1) is an increasing function of theta in [0,pi/2]
fig 1: SOLUTION: = = = = Since and we have , therefore for Hence, is an increasing function of in
Find the value of x for which y={x(x-2)}^2 is an increasing function.
Given: [Applying Product Rule] = = ……….(i) Therefore, we have For taking (say), is decreasing. For taking (say), is increasing. For taking (say), is decreasing....
Show that (fig1) is an increasing function of x throughout its domain.
fig 1: solution: Given: = = = = ……….(i) Domain of the given function is given to be Also and From eq. (i), for all in domain and is an increasing...
Find the intervals in which the following functions are strictly increasing or decreasing:
(e) SOLUTION: (e) Given: Here, factors and are non-negative for all Therefore, is strictly increasing if And is strictly decreasing if Hence, is strictly increasing...
Find the intervals in which the following functions are strictly increasing or decreasing:
(c) (d) SOLUTION: (c) Given: = ……….(i) Now = 0 or Therefore, we have three disjoint intervals and For interval , from eq. (i), = < 0 Therefore, is strictly decreasing. For...
Find the intervals in which the following functions are strictly increasing or decreasing:
(a) (b) SOLUTION: (a) Given: ……….(i) Now Therefore, we have two sub-intervals and For interval taking (say), from eq. (i), < 0 Therefore, is strictly decreasing. For...
Find the intervals in which the function f given by f(x)=2x^3-3x^2-36x+7 is (a) strictly increasing, (b) strictly decreasing.
(a) Given: = ……….(i) Now or or Therefore, we have sub-intervals are and For interval taking (say), from eq. (i), > 0 Therefore, is strictly increasing in For...
Find the intervals in which the function f given by f(x)=2x^2-3x is (a) strictly increasing, (b) strictly decreasing.
Given: ……….(i) Now Therefore, we have two intervals and (a) For interval taking (say), then from eq. (i), > 0. Therefore, is strictly increasing in (b) For...
Show that the function given by f(x)=sinx is (a) strictly increasing (0,pi/2) (b) strictly decreasing (pi/2,pi) in (c) neither increasing nor decreasing in (0,pi)
Given: (a) Since, > 0, i.e., positive in first quadrant, i.e., in Therefore, is strictly increasing in (b) Since, < 0, i.e., negative in second quadrant, i.e., in Therefore, is...
Show that the function given by f(x)=e^2x is strictly increasing on R.
Given: = > 0 i.e., positive for all R Therefore, is strictly increasing on R.
Show that the function given by f(x)=3x+17 is strictly increasing on R.
Given: i.e., positive for all R Therefore, is strictly increasing on R.