Business Calculus

The function f(x)=4x+9x^-1 has one local minimum and one local maximum.

Question:
This function has a local minimum at x=______ with a value _______ and a local maximum at x=________ with value _______?

  1. 👍 0
  2. 👎 0
  3. 👁 355
  1. Take the derivative of the function f(x) and set it equal to zero. Solve for x

    f'(x) = 4 - 9x^-2. = 0
    4 = 9/x^2
    x^2 = 9/4
    x = +___ or - ___

    That tells you where the maxima and minima are. The second derivative tells you which it is. It is a maximum where f'(x) = 0 and f''(x) is negative.

    This is basic important stuff. You should be asking how to do them, not what the answers are. Otherwise you won't learn the subject.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −2 and a local minimum value of 0 at x = 1.

  2. Calculus

    Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical

  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

  4. calculus

    How to sketch the graph of a differntiable function y = f(x) that has the given properties.Local minimum at (1,1) and local maximum at (3,3)

  1. Alg 2 HELP!

    Identify the x-intercepts, local maximum, and local minimum of the graph of f(x)=x^3+2x^2-13x+10 I am confused on where to begin.

  2. Calculus

    Explain why or why not: 1. if f'(c)=0, then f has a local maximum or minimum at c. 2. if f''(c)=0, then f has an inflection point at c. 3. F'(x)=x^2+10 and G(x)=x^2-100 are antiderivatives of the same function 4. Between two local

  3. Math

    Use the given graph of the function on the interval (0,8] to answer the following questions. Where does the function f have a local maximum? Answer (separate by commas): x= Where does the function f have a local minimum? What is

  4. Calculus

    A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 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

  1. Calculus

    Answer the following questions for the function f(x) = sin^2(x/3) defined on the interval [ -9.424778, 2.356194]. Rememer that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A

  2. Calculus

    Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function.

  3. Calculus

    Find constants a and b in the function f(x)=axe^(bx)such that f(3/4)=1 and the function has a local maximum at x=3/4. a= b=

  4. Calculus (Urgent Help)

    Okay, I need major help! Can someone tell me if these statements are true or false ASAP please. Thank you. 1. If ƒ′(x) < 0 when x < c then ƒ(x) is decreasing when x < c. True 2. The function ƒ(x) = x^3 – 3x + 2 is

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