It took 14 seconds for a mercury thermometer to rise from - 19C to 100C 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 8.5"C/second. 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. [0, 14] (Type your answer in interval notation.) Is f(t) continuous on [0,14]? O A. Yes, because there are no jumps in temperature while the temperature is changing, and there are no values that the temperature must skip over. O B. No, because there are points of discontinuity on the temperature scale in the interval [0, 14]. O C. It is impossible to know because the graph of f(t) is not shown