If `f( x ) = ( ( a + x ) / ( b + x ) )^( a + b + 2x )` , then f'(0 )

If f(x)=((a+x)/(b+x))^(a+b+2x) then prove that f'(0)=[2log((a)/(b))+(b^(2)-a^(2))/(ab)]((a)/(b))^(a+b)

If f''(x) le0 "for all" x in (a,b) then f'(x)=0

If f(x) = |(0, x-a, x-b),(x+a, 0, x-c),(x+b, x+c, 0)| , then the value of f(0) is :

If f'(c)=(f (b)-f(a))/(b-a) , where f(x) =e^(x), a=0 and b=1 , then: c = ….

If B = [{:(-1, 0), (2, 4):}] " and " f(x) = x^(2) - 4x + 5, then find f(B).

The area bounded by f(x)=sin^2x and the x - axis from x = a to x = b , where f''(a)=f''(b)=0(AAa,b,in(0,pi)) is