The function `f(x)=sum_(k=1)^5 (x-K)^2` assumes then minimum value of `x` given by (a) `5` (b) `5/2` (c) `3` (d) `2`

Let f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2 then the value of f(5) equals

If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing for all values of x , then (a) K (b) K >1 (c) K (d) K >2

The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (d) x=1

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

The real number x when added to its inverse given the minimum value of the sum at x equal to 1 (b) -1 (c) -2 (d) 2

Find the maximum and minimum values, if any, of the functions given by f (x) = (2x – 1)^(2)+ 3

Let h(x)=|k x+5| ,then domainof f(x) be [-5,7], the domain of f(h(x)) be [-6,1] ,and the range of h(x) be the same as the domain of f(x). Then the value of k is. (a)1 (b) 2 (c) 3 (d) 4

Find the maximum and minimum values, if any, of the functions given by h(x) = sin(2x) + 5

Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7a tx=2. The derivative of the function f(x)-f(4x)a tx=1 has the value equal to (a) 19 (b) 9 (c) 17 (d) 14

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these