If `f(x)=4x^3-x^2-2x+1` and `g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1ltxle2}` then `g(1/4)+g(3/4)+g(5/4)` is equal to

If f(x) is defined on [2,2] by f(x) = 4x^2-3x+1 and g(x) = (f(-x)-f(x))/(x^2+3) then int_(-2)^2g(x) dx is equal to

If f(x)=x^3-4x+1 , then find f(0) .

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

If f(x)=x^3-x^2+100x+2002 ,t h e n a) f(1000)>f(1001) b) f(1/(2000))>f(1/(2001)) c) f(x-1)>f(x-2) d) f(2x-3)>f(2x)

Let f(x)=4x^(3)+x^(2)-4x-1 . The equation f(x)=0 has roots 1 and (-(1)/(4)) . Find the root of f'(x)=0 mentioned in Rolle's theorem.

If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 then f'(0) is equal to

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

Let f(x)=f_1(x)-2f_2 (x) , where ,where f_1(x)={((min{x^2,|x|},|x|le 1),(max{x^2,|x|},|x| le 1)) and f_2(x)={((min{x^2,|x|},|x| lt 1),({x^2,|x|},|x| le 1)) and let g(x)={ ((min{f(t):-3letlex,-3 le x le 0}),(max{f(t):0 le t le x,0 le x le 3})) for -3 le x le -1 the range of g(x) is

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).