Answer the question. 6) It took 25 seconds for the temperature to rise from 3deg

Question

Answer the question. 6) It took 25 seconds for the temperature to rise from 3degree F to 179 degree F when a thermometer was taken from a freezer and placed in boiling water. Although we do not have detailed knowledge about the rate of temperature increase, we can know for certain that at some time, the temperature was increasing at a rate of 176/25 degree F/sec. Explain. Provide an appropriate response. 7) If the derivative of an even function f(x) is zero at x = c, can anything be said about the value of f ' at x = -c? Give reasons for your answer.

Explanation / Answer

6) consider we started observation of temperature change at T= 3 F

so at t=0, T = 3F

after 25 sec at t=25 secs

T = 179 F

here change in temeperature = final - initial = 179-3 = 176 = dT in F

here change in time = final time - initial time = 25-0 = 25 = dt in sec

rate of change (either increase/decrease) = dT/dt = (T2-T1) / (.t2-t1) = {176 / 25 } F/sec

7)

here given f(x) is an even function

here

f(x) = f(-x)

now differentiate on both sides w.r.t. x we get

f'(x) = - f'(-x)

but at x=c , f'(c) = 0

so from above relation

f'(-c) = -f'(c) = zero

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