SOLUTION: Determine the location of each extremum of the function f(x)= x^3-1/2x^2-6x+4 f(x)= 3x^2-x-6 = x^2-x/3-2=0 that's all i got

Question 998301: Determine the location of each extremum of the function
f(x)= x^3-1/2x^2-6x+4
f(x)= 3x^2-x-6
= x^2-x/3-2=0 that's all i got

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Determine the location of each extremum of the function
f(x)= x^3-1/2x^2-6x+4
f(x)= 3x^2-x-6 ( = f'(x), not f(x) )
= x^2-x/3-2=0 that's all i got
------------
Set f' = 0
3x^2 - x - 6 = 0
The extrema are at the zeroes of f'(x)

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=73 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.59066729088626, -1.25733395755292. Here's your graph:

========================
Those are the x values for the max (negative value) and min (positive value).
Finding the y values is tedious, but just algebra.
RELATED QUESTIONS
f(x)=-x^2+4x-9 Find the vertex What is the extremum value of the... (answered by HyperBrain)

Determine whether each is a linear function or not. Identify the degree of the function,... (answered by Boreal,ikleyn,MathLover1)

Hi, i tried solving my assignments, please help me check if i did it right..Thanks in... (answered by Alan3354)

State the domain, range and determine if the relation is a function. 1.... (answered by solver91311)

Help me please! I don't know what to do! Identify the number of solutions or zeros.... (answered by stanbon)

list all possible rational zeros of the function f(x)=... (answered by stanbon)

find all zeros of the function.... (answered by ewatrrr)

Find a polynomial function of lowest degree with rational coefficients and the following... (answered by solver91311)

Directions: Determine whether each is a linear function or not. Check Yes if it is a... (answered by Solver92311,josgarithmetic,greenestamps)