calculus

posted by .

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] .
a. Find the absolute maximum and minimum values of f(x)
b. Find the intervals on which f is increasing.
c. Find the x-coordinate of each point of inflection of the graph of f.

  • calculus -

    sorry for the double post

  • calculus -

    f(x) = e^x (cosx)
    f'(x) = e^x(-sinx) + e^x(cosx)
    = e^x(cosx - sinx) = 0 for max/min values of f(x)
    so e^x = 0 , no solution
    or
    cosx - sinx = 0
    sinx= cosx
    sinx/cosx = 1
    tanx = 1
    x = π/4 or 5π/4

    f(0) = e^0(cos0) = 1
    f(2π) = e^(2π)(1) = e^(2π) = appr. 535.5
    f(π/4) = e^(π/4) (√2/2) = appr. 1.55
    f(5π/4) = e^(5π/4) cos 5π/4 = appr. -35.9

    take it from there

    b) the function is increasing when f'(x) > 0
    e^x(cosx - sinx) > 0
    since e^x > 0 for all x
    this results in cosx - sinx >0
    -sinx > -cosx
    sinx/cosx < 1
    tanx < 1
    So for the domain from 0 to 2π
    tanx < 1 for
    0 < x < π/4 OR π/2 < x < 5π/4 OR 3π/2 < x < 2π
    ( I looked at the tangent curve for these)

    c) take the derivative of f'(x)
    f''(x) = e^x(-cosx) + e^x(-sinx) + e^x(-sinx) + e^x(cosx)
    = -2e^x sinx
    = 0 for pts of inflection

    then sinx = 0
    x = 0 , π, 2π

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Sketch f (x) = x + cos x on [-2pie,2pie ]. Find any local extrema, inflection points, or asymptotes. And find the absolute maximum and absolute minimum values of f on the given interval. i cant seem to figure out how to solve this
  2. Calc

    Let f be the function given by f(x)=2ln(x^2+3)-x with domain -3 is less than or equal to x which is less than or equal to 5 a) Find the x-coordinate of each relative maximum point and each relative minimum point of f. Justify your …
  3. Calculus - Functions?

    #1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a …
  4. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  5. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  6. calculus

    2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of inflection …
  7. calculus

    3. Let f be the function defined by f(x)=ln(2+sinx) for pi<=x<=2pi a. Find the absolute maximum value and the absolute minimum value of f. Show the analysis that leads to your conclusion. b. Find the x-coordinate of each inflection …
  8. calculus

    I needed help with these FRQ in my APCalc course. Any help or walkthrough would be extremely helpful - thanks in advance. Let f be the function given by f(x)=3ln((x^2)+2)-2x with the domain [-2,4]. (a) Find the coordinate of each relative …
  9. Relative Extrema: AP Calculus

    Consider the function f(x)= (3/4)x^4-x^3-3x^2+6x Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. Determine the interval(s) where f(x) …
  10. AP Calculus

    Consider the function f(x) = 1/4x^4 - 5/3x^3 - 3/2x^2 + 15x - 3. A. Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. B. Determine the …

More Similar Questions