If f(x)=x^5-5 x^4+5 x^3-10 has its local maxima and minima at x=a and x=b respectively, then 2 a+b is equal to

Step-by-step solution

We have, aligned f(x) & =x^5-5 x^4+5 x^3-10 f^ (x) & =5 x^4-20 x^3+15 x^2 aligned For maxima or minima put f^ (x)=0 aligned 5 x^4-20 x^3+15 x^2 & =0 5 x^2 (x^2-4 x+3 ) & =0 5 x^2(x-3)(x-1) & =0 x & =0,1,3 f^ (x) & =20 x^3-60 x^2+30 x f^ (x) & =10 x (2 x^2-6 x+3 ) f^ (0) & =0 f^ (1) & =10(2-6+3) 0 aligned Local maxima at x=1 and local minima at x=3 Here, a=1, b=3 2 a+b=2+3=5