A differentiable function f(x) has a local maximum at x=0 . Let y=2 f(x)+a x-b . The function y has a relative maxima at x=0 for

Step-by-step solution

Given, y=2 f(x)+a x-b ....(i) Differentiating both side w.r. to x aligned d y d x & =2 f^ (x)+a(1) ....(ii) d^2 y d x^2 & =2 f^ (x) aligned ....(iii) y has a relative maxima at x=0 aligned & & ( d y d x )_ x=0 & =0 & & & & & 2 f^ (0)+a & =0 & & 2(0)+a & =0 & & a & =0 aligned Also, ( d^2 y d x^2 )_ x=0 0 aligned & 2 f^ (0) & 0 & f^ (0) & =0 aligned Clearly, y has relative maxima for a=0 and all values of b .