2. The function f(x) = x^{3} - 6x^{2} + 9x + 25 has

- Option : A
- Explanation :
f '(x) = 3(x

^{2}-4x+3) f ''(x)=6(x)-12 at x=1, f "(1) at x=3, f ''(3) = +ve

4. The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is

- Option : C
- Explanation : Since f(x) = (1/x) is not continuous in [- 3, 3] [- 4, 2] or [- 1, 1], The point of discontinuity is '0'. Only in [2, 3] the function is continuous, and differentiable hence mean value theorem is applicable in [2, 3].

5. If f(x) = | x | , then for interval [-1, 1] ,f(x)

- Option : C
- Explanation : Since f(x) = |x| is continuous in [-1, 1] but it is not differentiable at x = 0 ε (-1, 1)