Rate of Change of a Function - Page 3

  • A nursery determines the demand in May for potted plants is p=3-(x/1000). the cost of growing x plants is c(x)= 0.02x +4000, 0<x<6000. determine the marginal profit function.?
  • A point moves along the curve #y=2x^2+1# in such a way that the #y#-value is decreasing at the rate of 2 units per second. At what rate is #x# changing when #x=-3#?
  • A man 1.7m tall walks at the rate of 2 meters per minute towards a street light that is 10m above the ground a.) At what rate is the tip of his shadow moving? b.) At what rate is the length of the shadow changing?
  • The length xmetre of green anaconda snake which is t years old is given approximately by formula x=0.7underroot(2t-1) where 1<t<10 find dx/dy and the rate of growth of snake which is 5years old?
  • How can you find a function, if you already know the rate of change of the function?
  • Why is it important to know rates of change?
  • What is the "rate of change" of a function?
  • Are there different kinds of rate of change?
  • What is computing derivative definition and how do you use #f(x+h)-f(x)/h#?
  • What is the average rate of change of the function #f(x) = x^2+5x# from #x_1 = 1# to #x_2 =2#?
  • The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder?
  • What is the rate of change for #f(x)=-2cos(4x-3)# on the interval from #x=pi/4# to #x=pi/2#?
  • What is the average rate of change for the function over the interval, #f(x)= x^2+5x# between #x =6# and #x=9#?
  • A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall??
  • Demand for an item is #600,000# pounds with a variation as function of time #t# is given by sine function #ksin((2pi(t-70))/365)#. How much the manufacturer should uniformly produce?
  • F(x) = 7x^2 + 4, find and simplify using the derivative function f(a+h) -f(a)/ (h) ?
  • What is the derivative of f(x) = (x)(6^-2x)?