1. Determine the critical points (Clasify as maxima, minima), Inflection points and trace the y=16x+4x^2-x^4
2. Find the equation of tangent to the circle x^2 + y^2 = 9 and parallel to 2x + y= 10.

2.
First find a slope form for the given circle by implicitly differentiating with respect to x:



and solve for y':



Because the slopes are equal, the derivative form above, when evaluated at the point of tangency, should be equal to the slope of the given line, which is is -2. Note:




which means


Substitute this condition into the equation of the circle to solve for x, then find y by taking half of x.

1.y=16x+4x^2-x^4

Differentiate


Now solve for zeros (or critical numbers to f(x)) then study the sign to determine types of extrema.

Good luck!!

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Placement Calculus & Statistics::

, Why is that using using quadratic formula and completing square in getting the CPs would not yield the same value such as this:
Completing Square:
0=x²-2x+2

0= x²-2x+1=-2+1
(x-1)²=-1
x-1=±√-1
x=1±√-1

Quadratic Formula:
-1±√(-2)²-4(1)(2)
(2)(1)
-1±√-4
2

Your equations would look much better and be easier to post if you learnt some basic latex: http://www.mathhelpforum.com/math-help/latex-help/

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When you apply the quadratic formula, b = -2, so -b is 2. For some reason you start with a -1 in the numerator in your work.

Pull out the 4 from the square root as a 2, and you get:



Did you need the complex zeros?

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Placement Calculus & Statistics::

so from that I can conclude that from X+2=0, i can have X= -2, and for 1±√-1, how should I have this If it has plus and minus sign, how could i fit it in the parenthesis because both will yield a different value of y.

First Critical Point (-2, -48)
SEcond critical point (1±√-1,?)

TANGENT EQUATION OF CIRCLE
I dont understand what you mean about this? If i substitute X=2y to the X^2+Y^2=9 , i will get a y=(√9/5). then what will be the next?

Have you realised yet that are not real (I did point this out in my earlier post)? Surely the implied domain of is real numbers.

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What you do next is recall that x=2y and substitute the value of y ....

(By the way, please don't edit posts that have been replied to by adding slabs of new stuff. Make a new post in the thread).

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