A differentiable function `f(x)` has a relative minimum at `x=0.` Then the function `f=f(x)+a x+b` has a relative minimum at `x=0` for (a)all `a` and all`b` (b) all `b` if `a=0` (c)all `b >0` (d) all `a >0`

The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c) x=0 (d) x=1

The minimum value of the function f(x)=2|x-2|+5|x-3| for all "x"inR is

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

If f is a real- valued differentiable function such that f(x)f'(x) lt 0 for all real x, then

Prove that the function f(x) = x+1/x(x!=0) is decreasing for all x in (-1,0)uu(0,1) .

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

If f is a real-valued differentiable function such that f(x)f'(x)lt0 for all real x, then -

Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x is differentiable for all x inR . The positive value(s) of a is (are)

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot