Find the interval in which f(x) is positive or negative : f(x) = (x-1)(x-2)(x-3)

Let f(x)=((x-3)(x+2)(x+5))/((x+1)(x-7)) . Find the intervals were f(x) is positive or negative .

Let f(x)=((x-3)(x+2)(x+6))/((x+1)(x-5)) Find intervals where f(x) is positive or negative

Find the intervals in which f(x) is increasing or decreasing: (1). f(x)=x|x|, x in R (2). f(x)=sinx+|sinx|, 0 < x le 2pi

Find the values of x for which f(x) is positive if f(x)=(x^(2)-6x+5)/(x^(2)-5x+6) .

The interval in which f(x)=cot^(-1)x+x increases , is

Find the intervals in which f(x)=x/(logx) is increasing or decreasing

Let f(x)=sin^(-1)((2phi(x))/(1+phi^(2)(x))) . Find the interval in which f(x) is increasing or decreasing.

Find the intervals in which f(x)=x/(logx) is increasing or decreasing.

Find the intervals in which the function f given by f(x)=\ x^3+1/(x^3)\ ,\ x\ !=0\ \ is (i) increasing (ii) decreasing.

Find the interval in which the function f given by f(x)=x^(2)-2x+3 is (a) Strictly increasing (b) Strictly decreasing