" (ii) "f(x)=|x-2|+|x-4|" २Cन "Cn" थों "" (ब),"f'(3)=0

If f(x)=|x-2|+|x-4| show that f'(3) = 0

If f(x)= x^5+x^3-2x+3 ,Prove that f'(1)+f'(-1)=4f(0).

Given that f'(x)=4x^(3)-3x^(2)+2x-1 find f(x) if f(0)=0 .

if f(x)=3x^(2)+4,0<=x<=2 and f(x)=9x-2,2<=x<=4 then show that int_(0)^(4)f(x)dx=66

The function f(x) = x^3 - 6x^2 + ax + b is such that f(2) = f(4) = 0 . Consider two statements. (S1) there exists x_1, x_2 in (2,4), x_1 lt x_2 , such that f' (x_1) = - 1 and f'(x_2) = 0 . (S2) there exists x_3, x_4 in (2, 4), x_3 lt x_4 , such that f is decreasing in (2 , x_4) , increasing in (x_4,4) and 2f'(x_3) = sqrt3 f(x_4) .

The function f(x) = x^3 - 6x^2 + ax + b is such that f(2) = f(4) = 0 . Consider two statements. (S1) there exists x_1, x_2 in (2,4), x_1 lt x_2 , such that f' (x_1) = - 1 and f'(x_2) = 0 . (S2) there exists x_3, x_4 in (2, 4), x_3 lt x_4 , such that f is decreasing in (2 , x_4) , increasing in (x_4,4) and 2f'(x_3) = sqrt3 f(x_4) .

If f'(x)=4x^3-3x^2+2x+k and f(0)=1, f(1)=4 find f(x)

If f(x)=x^(3)+3x^(2)-2x+4, find f(-2)+f(2)-f(0)