MATH

posted by .

Create a graph of a function given the following information:
The instantaneous rate of change at x = 2 is zero.
The instantaneous rate of change at x = 3 is negative.
The average rate of change on the interval 0 <x <4 is zero.

  • MATH -

    The instantaneous rate of change at x = 2 is zero.
    Means: A peak trough or inflection. The curve levels off there; the tangent is paralel to the x-axis.

    The instantaneous rate of change at x = 3 is negative.
    Means: There's a downward slop at x=3

    The average rate of change on the interval 0 <x <4 is zero.
    Means: It's symmetric over the interval - for every up there is a down, and you end as high as you start.

    Thus: It's a hill. Plot a parabola with a peak at x=2.

    Eg. Plot a curve between points:
    (0,0) (1,3) (2,4) (3,3) (4,0)

  • MATH -

    Good answer. They didn't actually ask for the function, so the above points (and also many other sets) will work.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Instantaneous and average rates of change

    a) Describe a graph for which the average rate of change is equal to instantaneous rate of change for its entire domain. Describe a real life situation that this graph could represent. b) Describe a graph which the average rate of …
  2. calculus

    i'm not sure how to do this. can someone help, please?
  3. Math

    Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x-1)(x+2)^2. a) Determine the function's average rate of change on -2<x<6. Answer; Avg rate of change is -3.2 b) Estimate …
  4. Math~Reinyyy

    Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x-1)(x+2)^2. a) Determine the function's average rate of change on -2<x<6. Answer; Avg rate of change is -3.2 b) Estimate …
  5. instantaneous rate of change problem

    Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
  6. Function: Rate of Change

    Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
  7. function rate of change

    Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
  8. rate of change

    Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π, …
  9. Instantaneous rate of change

    Please help.. Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change …
  10. Pre calculus/ Advanced Functions

    Samuel is investigating the rate of change of the function f(x) = cos x on the interval xE[0, 2pi]. He notices that the graph of f(x) passes through the x-axis at pi/2. He also determines the instantaneous rate of change at x = 0, …

More Similar Questions