1. ## critical point question

Trying to figure this out, but I am totally lost.

Question is...
the graph of y=2x^3 - ax^2 - bx + 5 has critical points x=2 and x=-1
find a and b

find and identify all local extremities

2. Originally Posted by timmy420
Trying to figure this out, but I am totally lost.

Question is...
the graph of y=2x^3 - ax^2 - bx + 5 has critical points x=2 and x=-1
find a and b

find and identify all local extremities
Critical points occur at values of x such that $\displaystyle \frac{dy}{dx} = 0$. Therefore $\displaystyle (x - 2)$ and $\displaystyle (x + 1)$ are factors of $\displaystyle \frac{dy}{dx} \, ....$

3. should i plug in the values and then do the dx/dy of it? Im totally stumped here.

4. Originally Posted by timmy420
should i plug in the values and then do the dx/dy of it? Im totally stumped here.
Get dy/dx.

(x - 2) and (x + 1) are its factors.

So dy/dx has the form A(x - 2)(x + 1).

The coefficient of x^2 is 6 therefore A = 6.

So dy/dx = 6(x - 2)(x + 1). Expand.

You now have two expresions for dy/dx. Compare the expressions and hence get the value of a and b.

5. Originally Posted by mr fantastic
Get dy/dx.

(x - 2) and (x + 1) are its factors.

So dy/dx has the form A(x - 2)(x + 1).

The coefficient of x^2 is 6 therefore A = 6.

So dy/dx = 6(x - 2)(x + 1). Expand.

You now have two expresions for dy/dx. Compare then and hence get the value of a and b.
Forget this. I have a better idea for you.

The two solutions to dy/dx = 0 are x = 2 and x = -1. Substitute these values of x to get two equation with a and b in them. Solve the resulting equations simultaneously.

6. by subbing them into it I get

2(2)^3-a(2)^2-b(2)+5 and 2(-1)^3 -a(-1)^2-b(-1)+5

if I set them equal to eachother I end up with 18= 3a + 3b
is this either bit on the right track?

7. Originally Posted by timmy420
by subbing them into it I get

2(2)^3-a(2)^2-b(2)+5 and 2(-1)^3 -a(-1)^2-b(-1)+5

if I set them equal to eachother I end up with 18= 3a + 3b
is this either bit on the right track?
You're meant to substitute x = 2 and x = -1 into dy/dx = 0.

Get two equations.

Solve simultaneously for a and b.