Question

From mean value theorem f(b) - f(a) = (b - a) f'(x₁); a < x₁ < b if f(x) = 1/x, then what is the value of x₁?

(A) √(ab)

(B) (a + b)/2

(C) 2ab/(a + b)

(D) (b - a)/(b + a)

Answer 1

Answer is (A) √(ab)

We have

f'(x) = -1/x²₁

Therefore,