Let `f(x)=x^(3)+ax^(2)+bx+5 sin^(2)x` be an increasing function on the set R. Then,

Leg f(x)=x^(3)+ax^(2)+bx+5sin^(2)x be an increasing function on the set R. Then find the condition on a and b.

Let f(x)=x^(3)+kx^(2)+5x+4sin^(2)x be an increasing function on x in R. Then domain of k is

Let f(x)=2x^(3)+ax^(2)+bx-3cos^(2)x is an increasing function for all x in R such that ma^(2)+nb+18 lt 0 then the value of m+n+7 is

Let f (x) = x ^(3) + ax ^(2) + bx + 5 sin ^2 theta + c be can increasing function of x (theta is a parameter), Then, a and b satisfy the condition:

condition that f(x)=x^(3)+ax^(2)+bx^(2)+c is anincreasing function for all real values of x' is

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

Suppose two numbers a and b are chosen randomly from the set {1, 2, 3, 4, 5, 6}. The probability that function f(x) = x^3+ ax^2 + bx is strictly increasing function on R is:

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then