Derivatives And Differentiation Equations Research Assignment - 275 Words

Derivatives And Differentiation Equations Research Assignment (Math Problem Sample) Content: 3.1 Tangents and the Derivative at a Point30. Balls changing volume: What is the rate of change of the volume of a ball (V=43r3) with respect to the radius when the radius is r=2?SolutionV=43r3Step 1; Now, differentiating w.r.t, RdVdR=43 (3R2)=4R2Step 2; Now just plug in 2 to find the rate of change of volume with respect radius when r=2inchdVdR4( 22)= 16Therefore the rate of change of volume is 163.4 The Derivative as a Rate of Change24. Marginal Revenue: Suppose that the revenue from selling x washing machines is rx=20,0001-1x dollars.a. Find the marginal revenue when 100 machines are produced.SolutionStep 1; Marginal revenue =Rate of change of revenue functionR'(x) =20000ddx (1 x )= 20000 x2Step 2; Marginal revenue when 100 machines are produced is:R'(100) = 20000 1002Step 3; marginal revenue = $2 dollarsb. Use the function r'(x) to estimate the increase in revenue that will result from increasing production from 100 machines to 101 machines a week.Solutio nThe marginal revenue function estimates the increase in revenue...