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 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

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.

A function is defined as f(x)=(x^2+1)/(3x-2) . Can f(x) take a value 1 for any real x ? Also find the value (s) of x for which f(x) takes the value 2.

if the function f(x)=AX-B X =2 is continuous at x=1 and discontinuous at x=2 find the value of A and B

If f(x)=x^3+x^2-a x+b is divisible by x^2-x , then find the value of a and b

The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (d) x=1

If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value of x.

If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find the least value of x^2+a x+b(x in R)dot