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.
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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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?Originally Posted by apcalculus