" (vii) "g(x)=(1)/(x^(2)+2)quad " (viii) "f(x)=x sqrt(1-x),0

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i) f(x)=x^2 (ii) g(x)=x^3-3x (iii) h(x)=sinx+cosx ,0ltxltpi 2 (iv) f(x) = sin x - cos x , 0 lt x lt 2pi (v) f(x) = x^3-6x^2+9x+15 (vi) g(x) = x/2 +2/x , x gt 0 (vii) g(x) = 1/x^2 +2 (viii) f(x) = x sqrt(1-x) , x gt 0

Describe fog and gof wherever is possible for the following functions (i) f(x)=sqrt(x+3),g(x)=1+x^(2) (ii) f(x)=sqrt(x),g(x)=x^(2)-1

Describe fog and gof wherever is possible for the following functions (i) f(x)=sqrt(x+3),g(x)=1+x^(2) (ii) f(x)=sqrt(x),g(x)=x^(2)-1

If (f(x))/(g(x))=h(x) where g(x)=sqrt(1-|(x^(2))/(x-1)|) and h(x)=(1)/(sqrt(|x-1|-[x])) then the domain of f(x)

Suppose f and g are two functions such that f,g:R rarr Rf(x)=ln(1+sqrt(1+x^(2))) and g(x)=ln(x+sqrt(1+x^(2))) then find the value of xe^(g(x))f((1)/(x))+g'(x) at x=1

If f(x)=(x)/(sqrt(1-x^(2))), g(x)=(x)/(sqrt(1+x^(2))) then (fog)(x)=

Suppose f and g are two functions such that f,g: R -> R f(x)=ln(1+sqrt(1+x^2)) and g(x)=ln(x+sqrt(1+x^2)) then find the value of xe^(g(x))f(1/x)+g'(x) at x=1

If f(x)=(x)/(sqrt(1-x^(2))),g(x)=(x)/(sqrt(1-2x^(2))) then (gof) (x) is