Expert: Paul Klarreich - 12/10/2008

Question
2. A) Use calculus methods to find the turning points of the function

F(x) =4x3-3x2-6x+2 and distinguish between them.






2. B) find dy/dx for the implicit function below:

x2y-xy2+x2+y2=0  

Answer
Questioner:   Emer
Category:  Calculus
Private:  No
 
Subject:  Mathematical methods for science1
Question:  2. A) Use calculus methods to find the turning points of the function
F(x) =4x3-3x2-6x+2 and distinguish between them.

...................................
Hi, Emer,

You didn't indicate what you already tried to do, so I assume you just need to get started.  Here is what you do:

2. A) Use calculus methods to find the turning points of the function
F(x) =4x3-3x2-6x+2 and distinguish between them.

Find F'(x), set it = 0, and solve.

For each solution, find F''(x) and draw the conclusions your text says to do:

F'' > 0, Min.
F'' < 0, Max,
F'' = 0, needs more work.

Try doing this. If you get stuck, send me what you did and I'll see what I can do.


2. B) find dy/dx for the implicit function below:

x2y-xy2+x2+y2=0

Implicit differentiation:

1. Differentiate each term.
2. If you have a product, like  x^2y or xy^2, remember to use the product rule.
3. Each term that has 'y' will give you a dy/dx.
4. Do the algebra necessary to solve for dy/dx.

Try doing this. If you get stuck, send me what you did and I'll see what I can do.