calc

find the values of a nad b if the function f(x)=2x^3 + ax^2 + bx + 36 has a local max when x=-4 and a min when x=5


First you calculate the derivative:

f'(x)=6x^2 + 2ax + b (1)

At the local maximum and minumum f' is zero. If a polynomial is zero at some point p, then it must contain a factor (x-p). So, since you know that f' is zero at both x =-4 and x = 5 you know that f' must be of the form:

f'(x) = A(x+4)(x-5) (2)

the two factors (x+4) and (x-5) make the right hand side a second degree polynomial, so A must be a constant. If f' were a third degree function then A would have been an unknown linea function. From (1) and (2) you find

6x^2 + 2ax + b = A (x+4)(x-5)

The coefficient of x^2 on the left hand side is 6, on the right hand side it is A, so you find that A = 6.

6 (x+4)(x-5) = 6 x^2 -6 x -120,

so 2a = -6 --> a = -3

and b = -120.

thanks!

it would help if you wrote the quistionbozo and by the way YOUR NOT KOOL

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. Math (Secant Lines)

    Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? -Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5. -Find the slope of each secant line -Use the results

  3. Calculus

    Consider the function f(x)=sin(5x)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= ( I need the values of f(x) for each x) (b) Based on your table of values, what

  4. Math 7A

    Use the function rule, y = 2x + 5, to find the values of y when x = 1, 2, 3, and 4. Write the answers as ordered pairs that would be used to graph the function. can someone help me i'm stuck on this question

  1. Algebra 2

    1. By graphing the system of constraints, find the values of x and y that maximize the objective function. 2

  2. 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

  3. Functions - math

    The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

  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

  1. Math (Limits)

    Consider the following function. f(x) = 2x^2 − 8x Find the limit. lim (Δx->0) (f(x+Δx)-f(x))/(Δx) How would I set up the equation to work with that function? I know how to plug in the values usually, but how would I do this

  2. algebra 1

    How do you determine if a mapping, table, or set of ordered pairs represents a function? A-all x values are different B-some x values repeat C-some y values repeat D-all y values are different I really have no clue what it is.

  3. 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

  4. algebra 2B

    5. Come up with a new linear function that has a slope that falls in the range −1 < m < 0 . Choose two different initial values. For this new linear function, what happens to the function’s values after many iterations? Are

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