Let `f(1)=-2a n df^(prime)(x)geq4. 2for1lt=xlt=6.` The smallest possible value of `f(6)` is 9 (b) 12 (c) 15 (d) 19

Let f(1)=-2, f'(x) ge4.2 for 1le x le6 . The smallest possible value of f(6)-16 is ……..

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)

Let f(1)-=a,f(3)=a^(2)&f'(x)<=6AA x in[1,3] ther greatest possible value of 'a' is-

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

The range of values of a for which the function f(x)={-x^3+cos^(-1)a , 0lt=x<1x , 1lt=xlt=3 has the smallest value at x=1, is [cos2, 1] (b) [-1,cos2] [0, 1] (d) [-1, 1]

If the function f(x)=x^(4)+bx^(2)+8x+1 has a horizontal tangent and a point of inflection for the same value of x then the value of b is equal to -1 (b) 1 (c) 6 (d) -6

Let f(x)=2x^(2)-12x+a, where a is a real constant.If smallest value of f(x) for x[1,2] is -2 then a=

Let f(x)=2x^(2)-12x+a, where a is a real constant.If smallest value of f(x) for x[1,2] is -2 then a=

If f(x) = 3x-1 when x geq 1 and f(x) = -x when x lt 1 then value of f(-2) is

If f(x) = 3x-1 when x geq 1 and f(x) = -x when x lt 1 then value of f(-2) is