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

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

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

If (7,x) (-3,3) (2,2) are collinear then the value of x is:

Find the range of f(x)=sgn(x^2-2x+3)dot

Discuss the maxima and minima of the function f(x)=x^(2/3)-x^(4/3)dot Draw the graph of y=f(x) and find the range of f(x)dot

Discuss the maxima and minima of the function f(x)=x^(2/3)-x^(4/3)dot Draw the graph of y=f(x) and find the range of f(x)dot

f(x)=e^x-e^(-x)-2sinx-2/3x^3dot Then the least value of n for which (d^n)/(dx^n)f(x)(""|)_(x=0)i snon z e roi s (a) 5 (b) 6 (c) 7 (d) 8

consider the function f(X) = 3x^(4)+4x^(3)-12x^(2) The range of values of a for which f(x) = a has no real