Mark the correct A. increases on [0, a]

B. decreases on [0, a]

C. increases on [–a, 0]

D. decreases on [a, 2a]

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a, b) is that f’(x)>0 for all x(a,b)

ϕ(x) = f(x) + f(2a – x)

ϕ’(x) = f’(x)-f’(2a – x)

ϕ’’(x) = f’’(x) + f’’(2a – x)

checking the condition

ϕ(x) is decreasing in [0,a]