Answer to Question #258883 in Calculus for hgjuf

Question

f​ 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.

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​(Type your answer in interval​ notation.)

Answer 1

It took 16 seconds for a mercury thermometer to rise from −20°C to 100°C when it was taken from a freezer and placed in boiling water.

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?

The closed intercal for this application is $[0, 16].$

Use the Mean Value Thorem

The function $f(t)$ is continuous on $[0, 16].$

The function $f(t)$ is differentiable on $(0, 16).$

Then there is a number $c$ in $(0, 16)$ such that

$$f'(c)=\dfrac{f(16)-f(0)}{16-0}=\dfrac{100-(-20)}{160}=0.75 \degree C/s$$