SOLUTION: (a) The equation of the curve is y=2x³-7x²+4x+4. Find the x value of the maximum turning point. The maximum T.P is NOT on the Y axis So far I have that dy/dx=6x²-14x+4=0 div

Algebra.Com
Question 430167: (a) The equation of the curve is y=2x³-7x²+4x+4. Find the x value of the maximum turning point. The maximum T.P is NOT on the Y axis
So far I have that dy/dx=6x²-14x+4=0
divide through by 2 3x²-7x+2=0
(3x-1)(x-2)=0
x=1/3 and x=2
When I sub 2 into y=2x³-7x²+4x+4, I get that y=0 therefore it must be x=1/3. I sub this into y=... and get 124/27.
I am unsure if this is correct.
(b) Factorise 2x³-7x²+4x+4. I used synthetic division and got that x=2 so (x-2)
∴ (x-2)(2x²-5x+2)
=(x-2)(2x-1)(x-2)
Now I am stuck. The qusetion is State the co-ordinates of the point A and hence find the values of x for which 2x³-7x²+4x+4<0.
It may be easier if I email you the question.
Any help would be greatly appreciated.
Andrew.

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 
Hi
1) correct on (1/3,124/27)being the maximum turning point |good work
2) 2x³-7x²+4x+4 = (x-2)(2x^2-3x-2) = (x-2)(2x+1)(x-2) |x= -1/2 and x = 2
x < -1/2 lends to f(x)< 0
always recommend sketching the graph..can be extremely helpful.
can download FREE graph software at
http://www.padowan.dk.com


RELATED QUESTIONS

Determine the coordinates (x,y) of the turning point of the curve y=x lnx - 2x, and... (answered by htmentor)
Workout the gradient and turning point p (x, y) of the curve y=ax^2+bx+c.use the turning... (answered by Fombitz)
The question is: The quadratic function f is defined by f(x) = {{{4x^2 +5x +2}}} a) (answered by Alan3354)
Find the equation of the line tangent to the curve at the point defined by the given... (answered by Alan3354)
when x=2, the value of f(x)=x^2-4x+4=0. This makes (2,0)a ? ____ of the quadratic... (answered by ewatrrr)
The curve whose equation is y= (2x2+3s-9)(x-k), where k is a constant, has a turning... (answered by Greenfinch)
Find the coordinates of the turning points of y = x^2/(x+1) . Determine in each case... (answered by MathLover1)
find the maximum value of the function f(x)= 3+4x^2-x^4 hint: let... (answered by drcole,richard1234)
If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4? (answered by ikleyn)
If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t... (answered by rothauserc)