it took 26 seconds for the temperature to rise from 7 degres F to 190 degrees F

Question

it took 26 seconds for the temperature to rise from 7 degres F to 190 degrees F when a thermometer was taken out of a freezer and placed in boiling water. although we do not have detailed knowledge about the rate of temperature increase we can know for certian that at some time the temperature was increasing at a rate of 183/26 degrees F/sec. Explain in detail using the mean value theorem

Explanation / Answer

let a state (x,y) is defined by (time, temperature) at state 1--> (0,7) at state 2 --> (26,190) from mean value theorem, there is atleast one point between these two states, such that derivative or rate (dy/dx) is equal to c=(y2-y1)/(x2-x1) or c=(190-7)/(26-0) =183/26

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