SOLUTION: Part of the graph to a curve has equation y=x�-15/2x�+12x-18. (a) Find the coordinates of the stationary point E. (b) Find the coordinated of G. G is on the X axis so Y=0.

Question 397318: Part of the graph to a curve has equation y=x�-15/2x�+12x-18.
(a) Find the coordinates of the stationary point E.
(b) Find the coordinated of G.
G is on the X axis so Y=0.
So far I have that
y=x�-15/2x�+12x-18
so dy/dx of y=x�-15/2x�+12x-18= 3�-15x+12
Now, At SP, dy/dx=0
∴ 3x�-15x+12=0
�3
x�-5x+4=0
(x-4)(x-1)=0
x=4 or x=1
Sub x=4 into x�-15/2x�+12x-18 and x=1 into x�-15/2x�+12x-18
4�-15/2(4)�+12(4)-18. 1�-15/2(1)+12(1)-18
64-120+48-18. 1-15/2+12-18
=-26. =-25/2

(4,-26). (1,-25/2)
Now I am compltely stuck.
Can someone please help me.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

It should be pretty obvious which of the two points is E. If E is the local maximum as marked on your graph, then the coordinates of E are

. Otherwise the coordinates of E are

But just to make sure, take the second derivative:

Then

is a local maximum, and

is a local minimum.

If G is on the x-axis, then G is the single real root. If the x-coordinate of G is a rational number, then the Rational Roots Theorem says that the root must be

The process is to use synthetic division to test each of the potential rational roots until you find one or have tested them all and concluded that there is no rational root. In this case there is one, but I'll let you find it for yourself. If you need a refresher on synthetic division, go to:

Purple Math - Synthetic Division

Make sure you read all four pages.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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