Let C be the curve `f(x)=ln^2x+2lnx` and `A(a,f(a)), b(b,f(b))` where `(a

The value of 'c' in Rolle's theorem for f(x) = log ((x^(2) + ab)/(x(a+b))) in (a,b) where a gt 0 is

Let f be continuous on [a, b] and assume the second derivative f" exists on (a, b). Suppose that the graph of f and the line segment joining the point (a,f(a)) and (b,f(b)) intersect at a point (x_0,f(x_0)) where a < x_0 < b. Show that there exists a point c in(a,b) such that f"(c)=0.

Verify Rolle theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}on[a , b], where 0

Verify Rolle theorem for the function f(x)=log{(x^(2)+ab)/(x(a+b))} on [a,b], where 0

Let g(x) be the inverse of the function f(x)=ln x^(2),x>0 . If a,b,c in R ,then g(a+b+c) is equal to

The range of the function f(x)=x^(2)ln(x)" for "x in [1, e]" is " [a, b] , where a+b is equal to

The range of the function f(x)=x^(2)ln(x)" for "x in [1, e]" is " [a, b] , where a+b is equal to

The constant c of rolle's theorem for the function f(x)="log" (x^2+ab)/((a+b)x) in [a,b] where 0 notin[a,b] is

Verify Rolles theorem for the function f(x)=log{(x^(2)+ab)/(x(a+b))} on [a,b], where ' 0

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