Let `f(x)=x^3+a x^2+b x+5sin^2x` be an increasing function on the set `Rdot` Then find the condition on `a` and `b`.

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

If f(x)=x^3+a x^2+b x+5sin^2x\ is a strictly increasing function on the set of real numbers then a and b must satisfy the relation:

Find the value(s) of a for which f(x)=x^3-a x is an increasing function on Rdot

Let f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+cos^(4)x)dx be an increasing function of x""inRandbinR , then " a " can take value(s)

Let f(x) = ax^3 + bx^2 + cx + d sin x . Find the condition that f(x) is always one-one function.

Prove that f(x)=a x+b , where a , b are constants and a >0 is an increasing function on Rdot

Show that f(x)=e^(2x) is increasing on Rdot

Show that the function f(x)=2x+3 is strictly increasing function on Rdot

Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in R and is strictely increasing function. If the range of a is [(m)/(n),oo), then find the minimum vlaue of (m- n).

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)