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`

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'.

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

Prove that f(x)=(x^3)/4-sinpix+3 takes the value of 7/3 for x in [-2,2]dot

Prove that f(x)=(x^3)/4-sinpix+3 takes the value of 7/3 for x in [-2,2]dot

Prove that f(x)=(x^3)/4-sinpix+3 takes the value of 7/3 for x in [-2,2]dot

It is given that the Rolles' theorem holds for the function f(x)=x^3+b x^2+c x ,x in [1,2] at the point x=4/3dot Find the values of b and c

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-

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-