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

Prove that f(x) = x^(2) -x + 1 is neither encreasing nor decreasing in [0,1]

Prove that f(x)=x-sinx is an increasing function.

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Prove that f(x)=(x^3)/4-sinpix+3 takes the value of 7/3 for x in [-2,2]dot

Statement 1: Let f(x)=sin(cos x)in[0,pi/2]dot Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]

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) .

Find the range of f(x) = (sinx)/(x)+(x)/(tanx) in (0,(pi)/(2))

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .