Let `g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot` Then find the interval in which `g(x)` increases.

Let g(x)=f(logx)+f(2-logx) and f^(prime prime)(x)<0AAx in (0,3)dot Then find the interval in which g(x) increases.

Let g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) increases in (a) (1/2,2) (b) (4/3,2) (c) (0,2) (d) (0,4/3)

If f(x)=log_(x^(2))(logx) ,then f '(x)at x= e is

Let h(x)=f(x)=f_(x)-g_(x) , where f_(x)=sin^(4)pix and g(x)=In x . Let x_(0),x_(1),x_(2) , ....,x_(n+1_ be the roots of f_(x)=g_(x) in increasing order. In the above question, the value of n is

If f(x)=log_x(lnx) then f'(x) at x=e is

intdx/(x[(logx)^2+4logx-1])

int(dx)/(x.logx.log(logx))=

The differential coefficient of f(logx) with respect to x , where f(x)=logx is (a) x/(logx) (b) (logx)/x (c) (xlogx)^(-1) (d) none of these

Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ^(2). Let n be the numbers of real roots of g(x) =0, then:

Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)(0)=3. Find f^(prime)(5)dot