6) 6 Distance x (cm) Temperatuire 100 93 70 6255 A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of thetemperature T(x), in degrees Celsius (...
6) 6 Distance x (cm) Temperatuire 100 93 70 6255 A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of thetemperature T(x), in degrees Celsius (°C), of the wire χ cm from the heated end. The function T is decreasing and is twice differentiable. a. Estimate T'(C7). Show the work that leads to your answer. Indicate units of measure b. Write an integral expression in terms of T(x) for the average temperature of the wire. Estimate the average temperature of the wire using a trapezoidal sum with four subintervals indicated by the data in the table. Indicate units of measure c. Find T'()dx, and indicate units of measure. Explain the meaning of 1 T()dx in terms of the temperature of the wire. Are the data in the table consistent with the assertion that T"(x) > 0 for every x in the interval。 x < 8? Explain your answer d.
6) 6 Distance x (cm) Temperatuire 100 93 70 6255 A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of thetemperature T(x), in degrees Celsius (°C), of the wire χ cm from the heated end. The function T is decreasing and is twice differentiable. a. Estimate T'(C7). Show the work that leads to your answer. Indicate units of measure b. Write an integral expression in terms of T(x) for the average temperature of the wire. Estimate the average temperature of the wire using a trapezoidal sum with four subintervals indicated by the data in the table. Indicate units of measure c. Find T'()dx, and indicate units of measure. Explain the meaning of 1 T()dx in terms of the temperature of the wire. Are the data in the table consistent with the assertion that T"(x) > 0 for every x in the interval。 x