It took 14 seconds for a mercury thermometer to rise from - 19"C to 100'C when it was taken from a freezer and placed in boiling water. Show that somewhere along the way the mercury was rising at the rate of 8.5C/second. . . . Use the Mean Value Theorem. Suppose y = f(x) is continuous on a closed interval [a, b] and differentiable on the interval's interior (a,b). Then there is at least one point c in (a, b) at which the following is true. f(b) - f(a) -= f'(c) b - a If f(t) is the function that represents the temperature shown on the thermometer after t seconds, what is the closed interval for this application? Assume that the thermometer is at the starting temperature at time t = 0. (Type your answer in interval notation.)