Friday
April 18, 2014

Homework Help: calc

Posted by kooldude on Thursday, November 9, 2006 at 10:18am.

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

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

math - find the values of a and b if the function y=2x^3+ax^2+bx+36 has a local ...
calculus - Find the cubic function f(x)=ax^3+bx^2+cx+d that has a local max ...
Math - What values of a and b make f(x) = x^3 + ax^2 + bx have a local max at x...
Calculus - A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx...
Calculus - A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx...
calc. - I'm having a lot of trouble with this problem: Sketch the graph and show...
Calculus - Find any absolute max/min and local max/min for the function f(x)=x^3...
Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
Calculus II - 1) Compute the indefinite integral: integral 2x ln(x^2 - 8x + 18) ...
calc - is the integral of 2x/(x^3-x) =-1/2ln(x+1)+1/2ln(x-1) I got this by doing...

Search
Members