Expert: Paul Klarreich - 10/5/2007

Question
How to find the x values of y= -8x^3 + 16x + 4. How many turning points are this function. Please help.

Thank you


Answer
Questioner:   Jeep
Category:  Advanced Math
Private:  No
 
Subject:  How to find the x values of y= -8x^3 + 16x + 4
Question:  How to find the x values of y= -8x^3 + 16x + 4. How many turning points are this function. Please help.

Thank you
............................................
Hi, Jeep,

I think you had some trouble asking the right questions here.

Second question: How many turning points does the graph of this function have?

dy/dx = -24x^2 + 16

Set that equal to zero:

-24x^2 + 16 = 0

x^2 = 2/3

x = +- sqrt(2/3)

It has two turning points.

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First one: Find the zeroes of the function -8x^3 + 16x + 4.  
OR: Find the x-intercepts of the graph of the function -8x^3 + 16x + 4.

[Either one is the same question.]

Try the inverse graph, just because the arithmetic is easier:

Solve  8x^3 - 16x - 4  = 0

This is a cubic equation and there is no easy way to find the solutions.  (There is a formula, but only about six people know it and I'm not one of them.)

So look for rational solutions.  They have the form a/b, where  a is a divisor of 4 and b is a divisor of 8.

A rough graph suggests that one of them is -1/4, which is of the proper form, so let's try it:


8(-1/4)^3 - 16(-1/4) - 4

8(-1/64) + 4 - 4

-1/8

Close, but no solution.  So I don't have an answer for this part.  Sorry.