[" If "f(x)={[ax^(3)+b,," for "0<=x<=1],[2cos pi x+tan^(-1)x,," for "1

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

If f(x)=ax^(2)+bx+c , show that , underset(hrarr0)"lim"(f(x+h)-f(x))/(h)=2ax+b

If f(x)={{:(e^(2x^(3)+x),x gt 0),(ax+b, x le 0):} is differentiable at x = 0, then

If f(x)={{:(e^(2x^(3+x)),x gt 0),(ax+b, x le 0):} is differentiable at x = 0, then

The function f(x) Is defined as follows : f(x)={{:(x^(2)+ax+b" , "0lexlt2),(3x+2" , "2lexle4),(2ax+5b" , "4ltxle8):} . If f(x) is continuous on [0,8], find the values of 'a' and 'b'.

If f(x) = ax^(3), show that xf'(x) - 3f(x) = 0.

If f(x)=(ax^(2)+b)^(3) , then the function g satisfying f(g(x))=g(f(x)) is given by

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is

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