A full tank of water springs a leak and empties in three hours. Water escapes the tank at a rate of g(t) gallons per hour, where t, 0

Question

A full tank of water springs a leak and empties in three hours. Water escapes the tank at a rate of g(t) gallons per hour, where t, 0<t<3, is measured in hours and g(t) is a continuous function. The selected values are: (0,48)(.5,36)(1,30)(1.5,28)(2,26)(2.5,24)(3,18) 

b) Use the data to find an approximation for g'(1.5).
c) For 0<t<3, must there be a time where g(t) = 25?

dumbcow · Answer

use slope definition here
$$g'(1.5) = \frac{g(t+h) -g(t)}{h}$$
based on available data points
use h=.5
$$g'(1.5) = \frac{g(2) -g(1.5)}{.5} = -4$$

anonymous · Answer

Part (b) is an application of the intermediate value theorem, I believe.