Let `f(x) =cos^-1 x^2+ cos^-1x`, then which one of the following is true? (A) `f (x)` is strictly decreasing (B) f (x) is decreasing in [0, 1] and increasing in [-1,0] (C) f(x) has only one local maxima. D) f(x) has only one local minima.

Which one of the following is true? For the function f(x)= cos x f is strictly decreasing in (pi, 2pi)

Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f(x)=0 has only one real root which is positive if a >1, b (b) f(x)=0 has only one real root which is negative if a >1, b>0. (c) f(x)=0 has only one real root which is negative if a (d) none of these

For the function f(x)\ =\ 1n\ (1-1n\ x) which of the following do not hold good? (a)increasing in (0,1) and decreasing in (1, e) (b) decreasing in (0,1) and increasing in (1, e) (c) x=\ 1 is the critical number for f\ (x) .(d) f has two asymptotes

Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f(x)=0 has only one real root which is positive if a >1, b 1, b>0. (c) f(x)=0 has only one real root which is negative if a <-1, b < 0. (d) none of these

Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f(x)=0 has only one real root which is positive if a >1, b 1, b 1, b > 0. (d) none of these

Let f(x)=sin x+ax+b. Then which of the following is/are true? f(x)=0 has only one real root which is positive if a>1,b 1,b 1,b>0. none of these

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Let f''(x)gt0 and phi(x)=f(x)+f(2-x),x in(0,2) be a function then the function phi(x) is (A) increasing in (0,1) and decreasing (1,2) (B) decreasing in (0, 1) and increasing (1,2) (C) increasing in (0, 2) (D) decreasing in (0,2)

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)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.