By solving the mean value theorem, the value of c in the interval (1,2) is 0.75.
Explanation:
The mean value theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one point c in (a,b) where the equation f'(c) = (f(b) - f(a))/(b - a) is satisfied.
For the specified interval (1,2) and given equation 1.2/x - 1.6, we can rearrange the equation to solve for c:
1.2/c - 1.6 = 0
1.2/c = 1.6
c = 1.2/1.6
c = 0.75
Therefore, the value of c in the interval (1,2) is 0.75.
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