Test on Application of Derivatives-3

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f’(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5)

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

If f and g are differentiable functions in [0, 1] satisfying f(0) = 2= g(1), g(0) = 0 and f(1) = 6, then for some c ∈ ]0, 1[

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :