Expert: Paul Klarreich - 4/26/2007

Question
question1

Determine the x co-ordinates of the turning points of the functions

(ii) y=4x^3-15x^2-18x+12

DY
--- = ??? D^2Y / D^2X
DX


AM TRYING TO FIND A QUICK WAY IN  DETERMINING THE X CO-ORDINATES.OF THE TURNING POINT.



Question 2

Find the equation of the straight line passing through the points

(2,4)and (4,-2)

Y2-Y1
-----
X2-X1

i would be greatful to see your answer  

Answer
Questioner:   Pearl
Category:  Advanced Math

Subject:  calculating the turning point
..................................................
Hi, Pearl,

1. Determine the x co-ordinates of the turning points of the functions

(ii) y=4x^3-15x^2-18x+12

DY
--- = ??? D^2Y / D^2X
DX


I AM TRYING TO FIND A QUICK WAY IN DETERMINING THE X CO-ORDINATES.OF THE TURNING POINT.
>> Sorry, but there is no quick way, in general.  The usual method is:

-- Find the first derivative,  dy/dx
-- Set that to zero.
-- Solve.  The solutions are (probably) your turning points. (Their x-coordinates, anyway.)

y=4x^3-15x^2-18x+12

dy/dx = 12x^2 - 30x - 18

12x^2 - 30x - 18 = 0
2x^2 - 5x - 3 = 0

(2x + 1)(x - 3) = 0
x = -1/2  and  x = 3


Question 2

Find the equation of the straight line passing through the points

(2,4)and (4,-2)

Y2-Y1
-----
X2-X1

That will determine the slope of the line. (You need it.)

Y2-Y1   - 2 - (4)
----- = --------- =
X2-X1    4 - 2

- 6
--- = -3
2

Now use the Point-slope Form of the equation of a line:

y - y0 = m(x - x0)

where (x0,y0) is any point on the line, such as (2,4)

y - 4 = -3(x - 2)

Simplify that up and you are done.