How to describe the motion, and velocity of a moving man

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.15 times a second. a tack is stuck in the tire at a distance of 0.373 m from the rotation axis. noting that for every rotation the tack travels one circumference (a) find the tack's tangential speed. (b) what is the tacks radial acceleration?

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)