How to find increasing and decreasing intervals using derivatives

Using a pedometer, you walk 3000 steps in 20 minutes, so your speed is 150 steps/min. each of your steps is 0.7 m long. what is your speed? 150 steps/min=/s=/h

Tall pacific coast redwood trees can reach heights of about 100 m. if air drag is negligibly small, how fast is a sequola cone moving when it reaches the ground f it dropped from the top of a 100 m tree?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)