calculus

h(t)=cot t

a.) [pi/4,3pi/4] b.) [pi/6,pi/2]

Find the average rate of change of the function over the give n interval and intervals. Please show step by step instructions.

Thanks

  1. 👍 2
  2. 👎 0
  3. 👁 2,112
  1. The average rate of change = ( y2 - y1 ) / ( x2 - x1 )

    a.)

    x1 = π / 4

    x2 = 3 π / 4

    y1 = cot ( π / 4 ) = 1

    y2 = cot ( 3 π / 4 ) = - 1

    ( y2 - y1 ) / ( x2 - x1 ) =

    ( - 1 - 1 ) / ( 3 π / 4 - π / 4 ) =

    - 2 / ( 2 π / 4 ) =

    ( - 2 / 1 ) / ( 2 π / 4 ) =

    - 2 ∙ 4 / 1 ∙ 2 π =

    - 4 / π

    b.)

    x1 = π / 6

    x2 = π / 2


    y1 = cot ( π / 6 ) = √3

    y2 = cot ( π / 2 ) = 0


    ( y2 - y1 ) / ( x2 - x1 ) =

    ( 0 - √3 ) / ( π / 6 - π / 2 ) =

    - √3 / ( π / 6 - 3 π / 6 ) =

    - √3 / ( - 2 π / 6 ) =

    ( - √3 / 1 ) / ( - 2 π / 6 ) =

    - √3 ∙ 6 / 1 ∙ ( - 2 π ) =

    - 6 ∙ √3 / - 2 π =

    - 2 ∙ 3 ∙ √3 / - 2 ∙ π =

    3 √3 / π

    1. 👍 2
    2. 👎 5
  2. Of course in this case you can write:

    The average rate of change = ( h2 - h1 ) / ( t2 - t1 )

    t1 = π / 4

    t2 = 3 π / 4

    h1 = cot ( π / 4 ) = 1

    h2 = cot ( 3 π / 4 ) = - 1

    ( h2 - h1 ) / ( t2 - t1 ) =

    ( - 1 - 1 ) / ( 3 π / 4 - π / 4 ) =

    - 2 / ( 2 π / 4 ) =

    ( - 2 / 1 ) / ( 2 π / 4 ) =

    - 2 ∙ 4 / 1 ∙ 2 π =

    - 2 ∙ 4 / 2 π =

    - 4 / π

    b.)

    t1 = π / 6

    t2 = π / 2

    h1 = cot ( π / 6 ) = √3

    h2 = cot ( π / 2 ) = 0

    ( h2 - h1 ) / ( t2 - t1 ) =

    ( 0 - √3 ) / ( π / 6 - π / 2 ) =

    - √3 / ( π / 6 - 3 π / 6 ) =

    - √3 / ( - 2 π / 6 ) =

    ( - √3 / 1 ) / ( - 2 π / 6 ) =

    - √3 ∙ 6 / 1 ∙ ( - 2 π ) =

    - 6 ∙ √3 / - 2 π =

    - 2 ∙ 3 ∙ √3 / - 2 ∙ π =

    3 √3 / π

    1. 👍 0
    2. 👎 0
  3. Bosnian, part b should be negative. Believe you solved as y2-y1/x1-x2 instead of y2-y1/x2-x1which would flip it to positive. Otherwise correct

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. pre-calculus--Please help, urgent.

    For the function f(x)= 8/x+7,find the average rate of change of f from 1 to x.

  2. calculus (rate of change)

    consider the function f(x)=x^2-6x+12 a. find the average rate of change over the interval [-1,3] b. use the definition of the derivative to find f prime(x) c. find the instantaneous rate of change at the point where x=3 d. find

  3. Algebra

    Find the average rate of change of f(x)=6x²−3 on the interval [2,a]. Your answer will be an expression involving a What I did so far: I found f(2) which is 21 and that would make the function (2,21) Then, I found f(a) which is

  4. math

    Let f be defined as follows. y = f(x) = x^2 - 4 x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 5 to x = 6 from x = 5 to x = 5.5 from x = 5 to x = 5.1 (b) Find the (instantaneous)

  1. calculus

    What is the instantaneous slope of y =8/x at x = -3? What is the average rate of change of y with respect to x over the interval [-3, 4] for the function y = 2x + 2? The surface area, S, of a sphere of radius r feet is S = S(r) =

  2. calculus

    Let f be the function defined by f(x)= sqrt(x), 0

  3. Calculus Please Help

    Given the numerical values shown for the function f(x), find approximate values for the derivative of f(x) at each of the x-values given. x= 0 1 2 3 4 5 6 7 8 f(x)= 13 15 16 17 17 14 11 9 7 f'(x)= 2 1 1 1 0 -3 -3 -2 -2 What seems

  4. Trigonometry

    Find the average rate of change for the function between the give values. f(x)=-4x + 8; from 1 to 2

  1. Math

    Find the average rate of change of the function f(x)=x^2+4x from x1=1 to x2=-7

  2. math

    The function gives the cost to manufacture x items. C(x) = 20,000 + 5x − x2 20,000 ; x = 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production

  3. MATH @Damon @ms. Sue

    Given the function f(x) = 2(3)^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average rate of change of each section. Part B: How many times greater is the average rate of change of

  4. Calculus

    1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given

You can view more similar questions or ask a new question.