Consider the function `f:(-oo, oo) -> (-oo ,oo)` defined by `f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2`. Which of the following is true?
A
f(x) is decreasing on [ -1,1] and has a local minimum at x = 1
B
f(x) is increasing on [-1,1] but has a local maximum at x = 1
C
f(x) is increasing on [ -1,1] but has neither a local maximum nor a local minimum at x =1
D
f (x) is decreasing on [ -1,1] but has neither a local maximum nor a local minimum at x= 1
Text Solution
Verified by Experts
Topper's Solved these Questions
MAXIMA AND MINIMA
ML KHANNA|Exercise MISCELANEOUS EXERCISE (MATCHING ENTRIES)|1 Videos
MATRICES
ML KHANNA|Exercise COMPREHENSION|3 Videos
MEASURES OF CENTRAL TENDENCY
ML KHANNA|Exercise ASSERTION / REASON|1 Videos
Similar Questions
Explore conceptually related problems
Consider the function f:(-oo,\ oo)->(-oo,oo) defined by f(x)=(x^2-a x+1)/(x^2+a x+1),\ 0
f:(-oo,oo)rarr(-oo,oo) defined by f(x)=|x| is
f:(-oo,oo)rarr(-oo,oo) defined by f(x)=x^(3)
Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1);0
Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (x^(2) - ax + 1)/(x^(2) + ax + 1) , 0 lt a lt 2 Let g (x) = underset(0) overset(e^(x))(int) (f'(t))/(1 + t^(2)) dt Which of the following is true ?
Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.
Consider the function f(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^(2)-a)/(x^(2)+a), agt0 which of the following is not true?
The function f : [0,oo)to[0,oo) defined by f(x)=(2x)/(1+2x) is
f:(0,oo)rarr(0,oo) defined by f(x)=x^(2) is
ML KHANNA-MAXIMA AND MINIMA -MISCELANEOUS EXERCISE (COMPREHENSION)
