3. The function H -1t0) gives the height of the water,in inches, in a bathtub at

Question

3. The function H -1t0) gives the height of the water,in inches, in a bathtub at time t, in minutes. Starting with an emply Starting with an empty tub at t-o, you plug the drain, take off your watch, turn on some relaxing music, enter the tub, and then begin to fill it at t neight of the water rises steadily until you turn off the water att 7. You relax in the tub, for the next 10 minutes, until at t 17 you stand in the tub to swat an annoying fly. As you stand, the water level lowers. Ater some a. What are the units of f'(t)? b. When are both f and f' positive? persisten a. The units of f'(t) are (1) b. For which of the value(s) of t are both f and f' positive? A. t-1 and t 4 OB, t=4and t = 19 C. t-1 and t#8 OD. t1 and t 19 (1) O inches per minute. O minutes. O inches. O minutes per inch.

Explanation / Answer

a. the unit of f'(t) are inches per minute (because it is showing height of water changing with respect to time)

b. f and f' bith are positive from the given options

at t = 4 and t = 19

because at t = 4 bathtub have some water means H= f(t) >0 and water is continuously filling it so height is increasing f'(t) > 0

because at t = 19 bathtub still having some water means H= f(t) >0 and but come out water drastically down the level but it will go up after some time

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