1. Questions

Math

What values of a and b make

f(x) = x^3 + ax^2 + bx

have a local max at x=-1 and a local min at x=3?

  1. 👍
  2. 👎
  3. 👁
Anonymous

  1. First of all, the derivative has to be zero at both x values. That requires
    3x^2 + 2ax + b = 0
    3 -2a +b = 0
    27 + 6a + b = 0
    8a = 24
    a = 3
    b = 2a -3 = 3
    This already determines a and b, but we had better make sure the max and min requirements are correct. Otherwise there is no solution.

    The second derivative is
    y''(x) = 6x + 2a. This is negative at x = -1 (therefore a relative maximum) and postive when x = 3 (therefore a relative minimum).

    We are OK with a = b = 3

    1. 👍
    2. 👎
    drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    This is the functions practice 1) which table of values does not represent a function? 2) given the function y=2x+3, what output values will result from the input values shown in the table? 3) which values for x and y will make

  2. Pre-Algebra

    Scatter plots are used to look for a pattern of association, or trend, between one set of values two sets of values three sets of values four sets of values My answer: two sets of values

  3. Geometry

    A. Find the values of a and b that would make the quadrilateral a parallelogram. B. Make sure to show work Top 6b-3 Left 2a+6 Right 3a-10 Bottom 5a+1 Thank you

  4. Math

    Name four values of b which make the expression factorable: x^2 - 3x + b

  1. math

    1. Select all the values of x that will make the following inequality true. 2(3x − 6) ≥ 5x − 10 x = -5 x = 1 x = 0 x = 2 x = 13 x = 7

  2. Calculus

    A rectangular sheet of metal measures 50cm by 40cm .Equal squares of side x cm are cut from each corner and discarded.The sheet is then folded up to make a tray of depth x cm.what is the domain of possible values of x.Find the

  3. Pre-Algebra

    Complete the sentence below. Scatter plots are used to look for a pattern of association, or trend, between ____________ A) one set of values. B) two sets of values. C) three sets of values. D) four sets of values. My Answer: B)

  4. algebra

    The mean of a data set is 7.8, the made is 6.6, and the median is 6.8. What is the least possible number of data values in the set? A 3 data values B 4 data values C 5 data values D 6 data values I'm not really sure how I'm

  1. Linear Algebra

    Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by

  2. Algebra

    Complete the table for each function. 1. f(x) = √x The x values are 0, 1,4 and 9. The corresponding y values that I got are 0, 1, 2 and 3. 2. g(x) = -1/4√ x The x values are 0, 1, 4, and 9. The corresponding y values that I

  3. math

    choose all values of x that would make the inequality true and how? 2/3 or 0.6 or 3/6 or 59% or 58x10_2

  4. Math, slope

    The cost of a taxi ride is $5.00 plus $0.75 for every 0.5 km. Graph this relation Identify the slope and the vertical intercept of the line. What do the represent? Write an equation relating the cost and the distance traveled. I'm

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