Let `f(x)=x^3-ax^2+bx+6` where `a,b in {1,2,3,4,5,6}`. The probability that `f(x)` is strictly increasing is

Let f(x)=3x-5, then show that f(x) is strictly increasing.

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:

The function f(x)=ax+b is strictly increasing for all real x is

A function f is such that f(x)=x^3+ax^2+bx+c , where a, b, c are chosen by throwing a die three times. The probability that f is an increasing function is

Let f(x)={x^(2);x>=0ax;x<0 Find real values of a such that f(x) is strictly monotonically increasing at x=0

If f(x)=ax^2+bx+2 , where f(-1)=7 and f(1)=5, then: f(a,b)-=

Prove that the function given by f(x)=2x^(3)-6x^(2)+7x is strictly increasing in R.

Let f(x) =x^(3) - 6x^2 +9x +18 , then f(x) is strictly decreasing in …………

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)

Let f(x)=ax^(2)+bx+c, where a,b,c in R,a!=0. Suppose |f(x)|<=1,x in[0,1], then