Let B15sqrtT as in Example 3 Estimate the instantaneous rate

Let B=15sqrt(T) as in Example 3. Estimate the instantaneous rate of change of B with respect to T when T=50.

(Note: Make sure to use at least 3 decimal places.)

Solution

given B=15T

B=15T^(1/2)

differentiate with respect to T

dB/dT=15(1/2)T^(1/2)-1

dB/dT=7.5T^(-1/2)

given T=50^o

dB/dT=7.5*50^(-1/2)

dB/dT=1.061

the instantaneous rate of change of B with respect to T when  T=50^o. is 1.061