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 f(x)=(x-a)^2(x-b)^2 , find f(a+b)

If f(x) =(x-a) (x-b) , then show that f(x) ge (a-b)^(2)/4

The function y=(a x+b)/((x-1)(x-4)) has turning point at P(2,1)dot Then find the value of a\ a n d\ bdot

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 int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

If int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

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

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