posted by .

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.


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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM?
  2. Calc

    1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)<0 if x<4 f'(4)=0 …
  3. Calculus

    Find the values for which f(x) = x^10-10x and if 0 (less than or equal) to x (which is less than or equal to) 2. a) f(x)has a local max or local min. Indicate which ones are max and which are mins. b) f(x) has a global max or global …
  4. calc.

    I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)-175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: …
  5. calculus

    I don't understand how to do this? I don't know the steps on how to do it! Can you please just tell me the steps?
  6. Calculus

    Find any absolute max/min and local max/min for the function f(x)=x^3-4x+5 on the interval [0,5). Made sure to prove that these points are max/min values. This is what I did so far. f'(x)=3x^2-4=0 3x^2=4 x= 2/sqrt3 The -2/sqrt3 is …
  7. calculus

    Find the local max/min values of f using botht the first and second derivatie test. I can do the first but I am having trouble with the second derivative. f(x)= x/(x^2+4) Help please...Thank you.
  8. Calc 1: Max/Min

    Find values for a and b so the function f(x)= ax*e^bx has the max value f(1)=3. Give exact values for a and b, not decimals)
  9. Math

    Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point f(x)= (7/4)x^4+(28/3)x^3+(-63/2)x^2-252x critical points in increasing order: …
  10. Calulus

    Consider the function y = 2x^3-3x^2+9x+5. 1. Find where the function is increasing, where the function is decreasing, and calculate all relative extrema (local max and local min) 2. Find where the function is concave up, where the …

More Similar Questions