Let `g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot` Then `(f(x+1))>g(f(x-1))` `f(g(x-1))>f(g(x+1))` `g(f(x+1))

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let g^(prime)(x)>0a n df^(prime)(x) g(f(x-1)) f(g(x+1))>f(g(x-1)) g(f(x+1))

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let f: R-> be a differentiable function AAx in R . If the tangent drawn to the curve at any point x in (a , b) always lies below the curve, then (a) f^(prime)(x)<0,f^(x)<0AAx in (a , b) (b) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (c) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (d) non eoft h e s e

Let f: R-> be a differentiable function AAx in R . If the tangent drawn to the curve at any point x in (a , b) always lies below the curve, then (a) f^(prime)(x)<0,f^(x)<0AAx in (a , b) (b) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (c) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (d) non eoft h e s e

Let f: R-> be a differentiable function AAx in R . If the tangent drawn to the curve at any point x in (a , b) always lies below the curve, then (a) f^(prime)(x)<0,f^(x)<0AAx in (a , b) (b) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (c) f^(prime)(x)>0,f^(x)>0AAx in (a , b) (d) non eoft h e s e

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)'(1)=2 b. G^(prime)'(1)=3 c. G^(prime)(1)=2 d. G^(prime)(1)=3

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)(1)=2 b. G^(prime)(1)=3 c. G^(1)=2 d. G^(1)=3