calculus

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

consider the function f(x0 = x^2 + 2x on the interval [-2, 2]

a. draw a sketch of the graph of f(x). find the average rate of change on the interval [-2, 2] and sketch this secant line.

b. find an expression that calculates the instantaneous rate of change of f(x) at any given point on the curve. find the coordinates on the graph of f(x) where the instantaneous rate of change equals the average rate of change.

c. write an equation for the tangent line at the point found in part b. sketch the tangent line on the same graph as part a. what is the relationship between the two lines on the graph?

thanks for the help in advance, i'm just really confused.

asked by zoe
  1. a.)Sorry but I cant post the link to the graph so you gotta do that part with a calculator

    To find average rate of change you need your two points with the given X values [-2,2]. Those points end up being (-2,0) and (2,8). Find the slope:
    (8-0)/(2-(-2))=8/4=2

    b.) Take derivative of your equation:
    f'=2x+2

    Since you wanna know where instantaneous rate of change and average rate of change are equal, set your derivative equal to your avg.:
    2=2x+2
    x=0
    Plug your new x value into the original equation to get your coordinates (0,0)

    c.)y=2x
    They should be parallel.

    p.s. I don't know if you need this, but the eqn. of your secant line is y=2x+4

    posted by michael

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis
  2. graph from asymptotes

    Is it possible to roughly sketch a graph(without plotting the points) from the asymptotes of a rational function? Is yes, what are the rules? For example, if I have to sketch a graph of y = (2x^2+10x-12)/x^2+x-6), how do I do it?
  3. calculus

    Give a reasonable sketch, on the axes provided, of the graph of the function x/(x^2-1)^1/2 showing all characteristics. Use the following pieces to justify your sketch. a) Domain ? b) coordinates x and y intercepts ? c) Symmetry ?
  4. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis
  5. maths

    1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2 2. Find the derivative of 2^x^2+log2(2x^2-1) 3. Use DeMeoivre's theorem to simplify the following expressions [(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin
  6. maths

    1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2 2. Find the derivative of 2^x^2+log2(2x^2-1) 3. Use DeMeoivre's theorem to simplify the following expressions [(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin
  7. Calculus

    Given the function f (x) = 3cos x for the interval 0 < x < 2 sketch the graph of the function
  8. Calculus I

    Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. 18. f(x) = 1/x , 1 < x < 3 I can graph it just fine, but for my answer I got that the function has none of the
  9. calculus

    Find the average rate of change of the function f(x) = 2x4 + 3x2 ¡ x + 2: (a) on the interval [0; 3] and (b) on the interval [¡2; 0]
  10. Calculus

    y=x^3-3x. Fill out the following table and then make a rough sketch of the graph. I can make the sketch just having trouble understanding what is wanted. y=0 when y'=0 when Relative Max(s) Relative Min(s) y'>0 on the

More Similar Questions