A differentiable function f(x) has a local maximum at x=0 . Let y=2 f(x)+a x-b . Which of the following is/are correct? 1. f^ (0)=0 2. f^ (0) 0 Select the correct answer using the code given below:

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) ....(iii) aligned f(x) has a local maximum at x=0 Hence, f^ (0)=0 and f^ (0) 0 ....(iv) Therefore option (C) is correct.