For the function x+(1x),x∈[1,3], the value of c for the mean value theorem is
1
3
2
None of these
Finding c using mean value theorem :
Let f(x)be an function define in interval [a,b] then M.V.T is given by f'(c)=f(b)-f(a)b-a
Letf(x)=x+(1x),x∈[1,3]f'(x)=1-1x2f'(c)=1-1c2(∵f'(c)=f(b)-f(a)b-a)b=3&a=11-1c2=(3+13)-(1+11)3-11-1c2=4321-1c2=231-23=1c213=1c2c=3
Hence, option (B) is correct answer.