Prove that `phi(x)=cos x` is a strictly monotonic decreasing function in `0 le x le pi`.

Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot

The function f(x)=cos x - 2ax is monotonically decreasing when-

A function f(x) is defined in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-

Show that the function f(x)=(3x+5)/(x+2) is strictly monotonic increasing in [0, oo) .

Show that each of the following functions is strictly increasing phi(x) = sin x(0 le x le pi/2)

If f'(x) exists and if f'(x) lt 0 everywhere in the interval a le x le b , then show that f(x) is a decreasing function in a le x lt b .

Prove that each of the following functions is strictly decreasing phi(x) = sin x(pi/2 le x le pi)

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

State when the function f(x) is said to be decreasing in a finite interval a le x le b .

Prove that the equation cos 2x + a sin x = 2a - 7 possesses a solution if 2 le a le 6 .