Show that the function `f(x)=(x-a)^2(x-b)^2+x` takes the value `(a+b)/2` for some value of `x in [a , b]dot`

If (x+2) (x-5) =x^(2)+(a+b) x+a xx b then value of (a+b) is

Verify Rolle's Theorem in the interval [a, b] for the function : f(x)=(x-a)^(2)(x-b)^(2) . Find the value of 'c'.

If the range of the function f(x)=3x^(2)+bx+c is [0,oo) then value of (b^(2))/(3c) is

The range of the function f(x)=cot^(-1)((sqrt(3)x^(2))/(1+x^(2))) is (a, b) then the value of b/a is

If the range of the function f(x)= cot^(-1)((x^(2))/(x^(2)+1)) is (a, b), find the value of ((b)/(a)+2) .

If the largest interval of x in which the function f(x)=x^(3)-3x+1 is decreasing is (a, b), then the value of a+2b is equal to

If (x-a,+2b)^(2)+(x-2a+b)^(2)=(a+b)^(2) then one value of x is

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b

If Rolle's theorems applicable to the function f(x)=(ln x)/(x),(x>0) over the interval [a,b] where a in I,b in I, then value of a^(2)+b^(2) can be:

If for the function f(x)=1/4x^2+b x+10 ;f(12-x)=f(x)AAx in R , then the value of ' b ' is-