Statement 1: Let `f(x)=5-4(x-2)^(2/3)dot` Then at `x=2,` the function `f(x)` attains neither the least value nor the greatest value. Statement 2: At `x=2,` then first derivative does not exist.

Find the derivative at x = 2 of the function f(x) = 3x .

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum nor minimum at x=2. Statement 2: If a function x=2 is a point of inflection, then it is not a point of extremum.

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)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Sketch the graph of a function f that satifies the given values: f(-2)=0 , f(2)=0 , lim_(x to -2) f(x)=0 , lim_(x to 2) f(x) does not exist.

Let f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1 Find the values of b for which f(x) has the greatest value at x=1.

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.