Let `f(x)=xsqrt(4a x-x^2),(a >0)dot` Then `f(x)` is a. increasing in (0,3a) decreasing in (3a, 4a) b. increasing in (a, 4a) decreasing in`(5a ,oo)` c. increasing in `(0,4a)` d. none of these

Show that f(x)=sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi) and neither increasing nor decreasing in (0,pi)

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then fis (A) increasing in (0,pi) and decreasing in (-oo,0)(B) increasing in (-oo,0) and decreasing in (0,oo)(C) increasing in (-oo,oo) and (D) decreasing in (-oo,oo)

Show that f(x)=cos x is decreasing function on (0,pi), increasing in (-pi,0) and neither increasing nor decreasing in (-pi,pi) .

Show that f(x)=cos x is a decreasing function on (0,pi), increasing in (pi,0) and neither increasing nor decreasing in (pi,pi) .

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,(pi)/(e)), decreasing in ((pi)/(e),oo) decreasing in (0,(pi)/(e)), increasing in ((pi)/(e),oo)

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)

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) then f(x)( a)increase in (0,oo)( b)decrease in [0,oo]( c)neither increases nor decreases in [0,oo]( d) increase in (-oo,oo)

Find the intervals in which f(x)=x^(4)-4x is increasing or decreasing.

Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)