What is the rate of change?

Question

The temperatures T (in °F) at which water boils at selected pressures p (in pounds per square inch) can be modeled by T = 87.97 + 34.96 ln p + 7.91 "radical p"

Find the rate of the temperature (in degrees per pounds per square inch) when the pressure is 40 pounds per square inch. (Round your answer to two decimal places.) 

Answer:_____ degrees per pound per square inch

Answer 1

T = 87.97 + 34.96lnp + 7.91√p

dT / dp = 34.96 / p + 3.955 / √p

So, when p = 40, dT / dp = 34.96 / 40 + 3.955 / √40 = 1.50

Answer 2

The rate of temperature change is the derivative of T wrt P

dT/Dp = d(87.97)/dp +34.96 d (ln(p)/dp + d(sqrt(p))/dp

That's equal to 0 + 34.96/p + 1/2(sqrt(p)

At p=40, this computes to 34.96/40 + 1/(2sqrt(40) = 4.03 degrees Fper PSI