Suppose that `f` is differentiable for all `x` and that `f^(prime)(x)lt=2fora l lxdot` If `f(1)=2a n df(4)=8,t h e nf(2)` has the value equal to 3 (b) 4 (c) 6 (d) 8

Suppose that f is differentiable for all x and that f'(x) le2" for all "x," If "f(1)=2 and f(4)=8 , then f(2)has the value equal to ……….. .

Let f be a differentiable function for all x and that |f'(x)|<=2 for all x. If f(1)=2 and f(4)=8 then compute the value of f^(2)(2)+f^(2)(3)

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

If f: RvecR is a differentiable function such that f^(prime)(x)>2f(x)fora l lxRa n df(0)=1,t h e n : f(x) is decreasing in (0,oo) f^(prime)(x) e^(2x)in(0,oo)

If f(x) is a differentiable function satisfying f^(')(x)lt2 for all xepsilonR and f(1)=2, then greatest possible integral value of f(3) is

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to

Let f be differentiable for all x, If f(1)=-2 and f'(x)>=2 for all x in[1,6] then find the range of values of f(6)

If f is twice differentiable such that f^(')(x)=-f(x) and f^(prime)(x)=g(x)dot If h(x) is twice differentiable function such that h^(prime)(x)=(f(x))^2+(g(x))^2dot If h(0)=2,h(1)=4, then the equation y=h(x) represents (a)a curve of degree 2 (b)a curve passing through the origin (c)a straight line with slope 2 (d)a straight line with y intercept equal to 2.