Mark the correct alternative in the following: Let ϕ (x) = f(x) + f(2a – x) and f’’(x) 0 for all x ϵ [0, a]. The, ϕ (x)

Question

Mark the correct alternative in the following: Let ϕ (x) = f(x) + f(2a – x) and f’’(x) > 0 for all x ϵ [0, a]. The, ϕ (x)

Philoid · Accepted Answer

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]

Mark the correct alternative in the following:Let ϕ(x) = f(x) + f(2a – x) and f’’(x) > 0 for all xϵ[0, a]. The, ϕ(x)

Mark the correct alternative in the following:
Let ϕ(x) = f(x) + f(2a – x) and f’’(x) > 0 for all xϵ[0, a]. The, ϕ(x)