Let S be the non-empty set containing all 'a' for which ` f (x) =( 4a-7)/3 x^3+(a-3) x^2 +x+5 `is monotonic for all ` x in R.` Find S.

Find all a in R s.t. the function f(X) = (a+2) x^3 - 3 ax^2 +9 ax - 1 decrease for all x in R.

The set of all values of a for which the function f(x)=((a^2-1)/3)x^3+(a-1)x^2+2x+1 increases on R, is

Let f (x) =x^(3) . Find the intervals of monotonicity.

Let f (x) =x^(3) . Find the intervals of monotonicity.

The set of all x for which the function h(x)=-log_(2)(-2x-3+x^(2)) is defined and monotonically increasing is

Let f(sin x)+2f(cos x)=3 for all x in R Fird f(x)

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.